Question

qns on permutations

Answer 1

anticipation .... quite an audience .....

Answer 2

ya plz wait

Answer 3

qns
qsn
nqs
nsq
sqn
snq

Answer 4

prove 33! is divisible by 2^15

Answer 5

how many even numbers from 2 to 32?

Answer 6

what mevere said!

Answer 7

?

Answer 8

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

Answer 9

didnt get you

Answer 10

that's 16 numbers

Answer 11

every time you have an even number it will contribute a factor of two to 33!

Answer 12

32/2 = 16

16/2 = 8

8/2 = 4

4/2 = 2

2/2 = 1

16 + 8 + 4 + 2 + 1 = 31 2's

Answer 13

then we could divide by 2^16 maybe even higher ....

Answer 14

what does this have to do with permutations?

Answer 15

how about this, find the greatest integer such that
\[2^n | 33!\]

Answer 16

\[\end\end\]

Answer 17

Can you something big?

Answer 18

i think it's 31

Answer 19

next :how many nos are there between 100 and 1000 in which all digits are distinct?

Answer 20

i don't know the answer, but i bet we could find it.
classify positive integers between 1 and 33 divisible by 2, 2^2, 2^3, etc

Answer 21

For the firs one use http://mathworld.wolfram.com/LegendresFormula.html and it's trivial.

Answer 22

you can write a 1-liner in Python to answer that

Answer 23

@AravindG, we have a lot of numbers that are divisible by 2.

If we have 4! then we know that at least
4! is divisible by 2^2 since 4! contains 2 and 4

If we have 6! then we know that at least
6! is divisible by 2^3 since 6! contains 2 and 4 and 6

If we have 8! then we know that at least
8! is divisible by 2^4 since 8! contains 2 and 4 and 6 and 8

Same thing for 33!

Answer 24

It's 31 im sure

Answer 25

how many nos are there between 100 and 1000 in which all digits are distinct?

Answer 26

@ffm i am confused about how legandre is going to tell me how many powers of two are in all numbers less than or equal to n. i am not saying it is not right, i am saying i don't understand how that is going to give it to me

Answer 27

Okay:

Prove \(33! \) is divisible by \(2^{15} \)

Now, we can use Legendre's Formula to show that that the maximum power of 2 that divides \( 33!\) is \(2^{31}\) Hence the proof. QED.

Answer 28

help me in next qn

Answer 29

sat, it's probably a corollary of the Legendre's formula.

Answer 30

now i have to think.

Answer 31

Next question
Find how many numbers are between 100 and 1000.

Then subtract that by the number of non-distinct numbers

Answer 32

>> how many nos are there between 100 and 1000 in which all digits are distinct?

Hint: Break the problem in two parts,

1.How many three digits are there with that constraints.
2.How many four digits are there with that constraints.

Answer 33

sat, It's a standard trick that we were taught as a mathlete so I am sure you will get it in jiffy :)

Answer 34

k

Answer 35

next one

Answer 36

i would start with a 3 digit number and say
we have 9 choices for the hundreds place, (1 through 9)
9 for tens place (0 through 9 , less what was in the first spot
8 for the ones place.
then repeat for numbers than 100
maybe there is a snappier way to do it

Answer 37

*less than

Answer 38

in how many ways can 6 woman draw water from 6 taps if no tap remains unused?

Answer 39

6! unless i am seriously confused

Answer 40

6!?

Answer 41

definately 6!

Answer 42

http://ideone.com/tWkFJ

Answer 43

there are 648 numbers between [100,1000] (including 100 and 1000) where the digits are unique

Answer 44

@ffm i assume you mean above "three digit numbers"

Answer 45

Yes sat :)

Answer 46

[102, 103, 104, 105, 106, 107, 108, 109, 120, 123, 124, 125, 126, 127, 128, 129, 130, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 150, 152, 153, 154, 156, 157, 158, 159, 160, 162, 163, 164, 165, 167, 168, 169, 170, 172, 173, 174, 175, 176, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198, 201, 203, 204, 205, 206, 207, 208, 209, 210, 213, 214, 215, 216, 217, 218, 219, 230, 231, 234, 235, 236, 237, 238, 239, 240, 241, 243, 245, 246, 247, 248, 249, 250, 251, 253, 254, 256, 257, 258, 259, 260, 261, 263, 264, 265, 267, 268, 269, 270, 271, 273, 274, 275, 276, 278, 279, 280, 281, 283, 284, 285, 286, 287, 289, 290, 291, 293, 294, 295, 296, 297, 298, 301, 302, 304, 305, 306, 307, 308, 309, 310, 312, 314, 315, 316, 317, 318, 319, 320, 321, 324, 325, 326, 327, 328, 329, 340, 341, 342, 345, 346, 347, 348, 349, 350, 351, 352, 354, 356, 357, 358, 359, 360, 361, 362, 364, 365, 367, 368, 369, 370, 371, 372, 374, 375, 376, 378, 379, 380, 381, 382, 384, 385, 386, 387, 389, 390, 391, 392, 394, 395, 396, 397, 398, 401, 402, 403, 405, 406, 407, 408, 409, 410, 412, 413, 415, 416, 417, 418, 419, 420, 421, 423, 425, 426, 427, 428, 429, 430, 431, 432, 435, 436, 437, 438, 439, 450, 451, 452, 453, 456, 457, 458, 459, 460, 461, 462, 463, 465, 467, 468, 469, 470, 471, 472, 473, 475, 476, 478, 479, 480, 481, 482, 483, 485, 486, 487, 489, 490, 491, 492, 493, 495, 496, 497, 498, 501, 502, 503, 504, 506, 507, 508, 509, 510, 512, 513, 514, 516, 517, 518, 519, 520, 521, 523, 524, 526, 527, 528, 529, 530, 531, 532, 534, 536, 537, 538, 539, 540, 541, 542, 543, 546, 547, 548, 549, 560, 561, 562, 563, 564, 567, 568, 569, 570, 571, 572, 573, 574, 576, 578, 579, 580, 581, 582, 583, 584, 586, 587, 589, 590, 591, 592, 593, 594, 596, 597, 598, 601, 602, 603, 604, 605, 607, 608, 609, 610, 612, 613, 614, 615, 617, 618, 619, 620, 621, 623, 624, 625, 627, 628, 629, 630, 631, 632, 634, 635, 637, 638, 639, 640, 641, 642, 643, 645, 647, 648, 649, 650, 651, 652, 653, 654, 657, 658, 659, 670, 671, 672, 673, 674, 675, 678, 679, 680, 681, 682, 683, 684, 685, 687, 689, 690, 691, 692, 693, 694, 695, 697, 698, 701, 702, 703, 704, 705, 706, 708, 709, 710, 712, 713, 714, 715, 716, 718, 719, 720, 721, 723, 724, 725, 726, 728, 729, 730, 731, 732, 734, 735, 736, 738, 739, 740, 741, 742, 743, 745, 746, 748, 749, 750, 751, 752, 753, 754, 756, 758, 759, 760, 761, 762, 763, 764, 765, 768, 769, 780, 781, 782, 783, 784, 785, 786, 789, 790, 791, 792, 793, 794, 795, 796, 798, 801, 802, 803, 804, 805, 806, 807, 809, 810, 812, 813, 814, 815, 816, 817, 819, 820, 821, 823, 824, 825, 826, 827, 829, 830, 831, 832, 834, 835, 836, 837, 839, 840, 841, 842, 843, 845, 846, 847, 849, 850, 851, 852, 853, 854, 856, 857, 859, 860, 861, 862, 863, 864, 865, 867, 869, 870, 871, 872, 873, 874, 875, 876, 879, 890, 891, 892, 893, 894, 895, 896, 897, 901, 902, 903, 904, 905, 906, 907, 908, 910, 912, 913, 914, 915, 916, 917, 918, 920, 921, 923, 924, 925, 926, 927, 928, 930, 931, 932, 934, 935, 936, 937, 938, 940, 941, 942, 943, 945, 946, 947, 948, 950, 951, 952, 953, 954, 956, 957, 958, 960, 961, 962, 963, 964, 965, 967, 968, 970, 971, 972, 973, 974, 975, 976, 978, 980, 981, 982, 983, 984, 985, 986, 987]

Answer 47

It is 6! for you next question.

Answer 48

@agd, that's one way to do it! grind it til you find it

Answer 49

see? One line in Python!

Answer 50

how many 6 digit telephone nos can be constructed with digits 0 1 2 3 4 5 6 7 8 9 if each no: starts with 35 and no digit appears more than once

Answer 51

all of your questions can be answered with the help of the itertools module in Python :-D

Answer 52

here is one line in my head
\[9\times 9=81, 81\times 8=648\]

Answer 53

Are you trying this problem even for a mint? Posting here is not going to help you.

Answer 54

enough with the python thing adgd!!!
lol

Answer 55

@satellite that's actually better than my python solution :-D

Answer 56

lol

Answer 57

I just discovered list comprehensions... if I'm already annoying with Python... wait till I discover things like replacing classes with dictionaries and the full power of the itertools and related modules :-D

Answer 58

but yeah avarind you have to try these problems yourself in order to understand them yourself :-D

Answer 59

I think you messed up moneybird, cant have 10 options for the first space since 3 and 5 have been chosen

Answer 60

ya

Answer 61

o i thought 3 and 5 are extra numbers

Answer 62

I dont know, are they arvind?