Question

What is the greatest power of 18 in 50C25

Answer 1

Mere ko dur dur tak koi idea nahin hain ki ye kiya hain.. please help :)

Answer 2

@ParthKohli

Answer 3

@satellite73

Answer 4

help me..... please !

Answer 5

\[^{50} C_{25} = \frac{50 !}{25! \times 25!}\]

Answer 6

By 50C25, this is what you mean??

Answer 7

I know this but I don't know WHAT THE POWER OF 18 IN 50C25 MEAN ?

Answer 8

@Luigi0210

Answer 9

@morgcarr12

Answer 10

WHY ARE SO MANY PEOPLE TAGGING ME IM SO CONFUSED, lol ill try to figure it out tho

Answer 11

\(\large 18 = 2\times 3^2\)
so the power of 3 is the limiting factor here

Answer 12

also notice that 50C25 is an integer because it represents number of ways of choosing 25 objects from 50 objects which is countable

Answer 13

Next, do you know how to get the highest exponent of 3 in the prime factorization of 50! ?

Answer 14

NO, :(

Answer 15

50! = 1.2.3.4.5.6.7.8...49.50

Answer 16

how many numbers less than 50 are multiples of 3 ?

Answer 17

15

Answer 18

OKAY ! WHAT TO DO FOR THE REST. :)

Answer 19

try again

Answer 20

number of multiples of 3 less than or equal to 50 = \(\large \left\lfloor\dfrac{50}{3}\right\rfloor = 16\)

Answer 21

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45= 15 nos only.

Answer 22

oha ya 48 =1 silly me :(

Answer 23

what about 48 ?

Answer 24

:)

Answer 25

so can we say the exponent of 3 in prime factorization of 50! is 16 ?

Answer 26

nope, because multiples of 3^2's contribute two 3's,
but we have counted them only once.

so lets count how many multiples of 3^2's are there

Answer 27

how many multiples of 3^2's are there ?

Answer 28

so, the exponent of a number let x in y! is all the multiple of x less than y right?

I don't know this, so inquired ?

Answer 29

consider a smaller example :

4! = 24 = 2^3*3^1

Answer 30

here the exponent of 2 is 3
and the exponent of 3 is 1

Answer 31

in 18 exponent of 3 is 2, than why did we find that for 50! Please explain me this.

Answer 32

we're trying to find out the exponent of 3 in 50!

Answer 33

because we want to see how many 3^2's are there in 50C25

Answer 34

okay let me conclude till here,

we first expressed 18 in exponential of primes,
we found it to be 3^2*2

now since we need to find the power of 18 in 50C25 so, we are finding the power of 3 in 50 and power of 3 in 25 correct.

Answer 35

our idea is this :
1) find the exponent of of 3 in 50!
2) find the exponent of of 3 in 25!

play with above to figure out the exponent of 3^2 in 50C25

Answer 36

you're right!

Answer 37

lets finish finding the exponent of 3 in 50! first

Answer 38

okay so, for 50! we will find the multiples of 3^2 less than 50 or the multiples of 3 less than 50. Cause in one our last post you said this, I could not figure out what you said,

"nope, because multiples of 3^2's contribute two 3's,
but we have counted them only once.

so lets count how many multiples of 3^2's are there"

Answer 39

Number of 3s in 50! is:

\[\frac{50}{3} + \frac{50}{3^2} + \frac{50}{3^3 } = 16 + 5 + 1\]

Answer 40

while counting multiples of 3, we did not account for numbers that have two 3's in them right ?

for example, the numbers 9 and 18 are counted only once
however they each contribute two 3's

Answer 41

okay so according to #waterineyes we have 22 3 in 50. than ?

Answer 42

similarly count number of 3's in 25!

Answer 43

25/3+25/3^2+25/3^3 this way ?

Answer 44

exactly !

Answer 45

take the integer value

Answer 46

measn if the value is 24.07 than i should take 24 ?

Answer 47

#means

Answer 48

yes

Answer 49

then ?

Answer 50

how many 3's are there in 25! ?

Answer 51

12.03 so, it will be 12. for 50 it is 24 not 22

Answer 52

nope

Answer 53

you need to take integer value for each fraction

Answer 54

ya for 50! according to the formula I found the value to be 24.07 than ?

Answer 55

\[\frac{25}{3} + \frac{25}{3^2} = 8 + 2 = 10\]

Answer 56

exponent of 3 in 50! :
\[\large \left\lfloor\dfrac{50}{3}\right\rfloor +\left\lfloor\dfrac{50}{3^2}\right\rfloor +\left\lfloor\dfrac{50}{3^3}\right\rfloor = 16+5+1 = 22\]

Answer 57

oho for each fraction i didnt notice that again.. Dhet teriki.. Silly me :(

Answer 58

okay so the value is 22+10=32

Answer 59

It will be simple for you to understand if you take it in another way..

Answer 60

Firstly divide 50 by 3, and tell me what did you get??

Answer 61

exponent of 3 in 25! :
\[\large \left\lfloor\dfrac{25}{3}\right\rfloor +\left\lfloor\dfrac{25}{3^2}\right\rfloor +\left\lfloor\dfrac{25}{3^3}\right\rfloor = 8+2+0 = 10\]

Answer 62

okay i got it so, now for 50 it is 22 and for 25 it is 10 then ?

Answer 63

Do not take the remainder, leave the remainder.. take only the quotient..

Answer 64

Okay got till here..

Answer 65

yes next lets see how can we use the information that we have to figure out the exponent of 3 in 50C25

Answer 66

whats 50C25 again ?

Answer 67

50!/25!*25!

Answer 68

When you divide 50 by 3, you will get 16 as quotient..

Now, divide this 16 again by 3, you will get 5..

Now divide 5 by 3, you will get 1..

Now you cannot divide now 1 by 3, so you get now : 16 + 5 + 1 = 22

Answer 69

okay that seems good @waterineyes

Answer 70

can we write that like this :

\[\large ^{50} C_{25} = \frac{50 !}{25!* 25!} = \dfrac{3^{22} a}{3^{10}b*3^{10}b}\]

?

Answer 71

so we have 3^2*a/b^2
understood till here. than ? :)

Answer 72

then we're done !

there is only one 9 in 50C25
what does that tell us ?

Answer 73

Similarly you can do it for 25..

25/3 = 8

8/3 = 2

As 2 < 3, so, now add : 8 + 2 = 10

Answer 74

it tells us that the answer is not matching with the solution where it is given to be 1

Answer 75

:/

Answer 76

:(

Answer 77

think a bit,
there is a one 9 as factor in 50C25 :

50C25 = 9*something

Answer 78

ya 9*a/b^2

Answer 79

that precicely means the highest exponent of 18 is 1, right ?

Answer 80

how come the last statement is depicted.

Answer 81

because there will always be more number of 2's than 3's

Answer 82

since only one 9 is available,
you can pull out only one 18 out of 50C25

Answer 83

if you want, you can find out the exponent of 2 as well..

Answer 84

can you provide me an algorithm to deal with such questions, seriously I have learnt it first time :) please. I mean how come the 18 at the last. :(

Answer 85

do you agree that the highest exponent of 3 in 50C25 is 2 ?

Answer 86

if so, next think about how many 3's are required for 18

Answer 87

since 50c25=9a/b^2 so the highest exponent shall be 2 only right ?

Answer 88

only thing I am stuck with is that,

we were asked to find the power of 18 in 50C25

we fist prime factorised 18 and than we found the power of 3 in 50 and 25 and which we found to be 9a/b^2

than after this we can conclude that
1. highest power of 3 is 2
2. highest power of 18 is 2-------------- How ????????

Answer 89

sorry typo of 18 is 1 how ?

Answer 90

how many 3's are needed to cookup one 18 ?

Answer 91

and how many 3's are available in 50C25 ?

Answer 92

2 3's are needed.

Answer 93

3^2*2

Answer 94

yes

Answer 95

and we have 3^2*a/b^2 which means we have 2 3's . So we can get only 1 18, this is what you mean.

Answer 96

Exactly !

Answer 97

to aisa bolo na.. okay,

so ever again if I am asked to find the power of some x in yCr
than I shall do this
1. prime factorise x let it be 3*2
2. find the exponent of either 2 or 3 in 50 and than in 25
3. express the yCr term
4. find the number of 3 or 2 I have and match with number of 2 and 3 I require to make x

yuhoo thats the answer number of x I can make.

Correct ?