Question

CHALLENGE QUESTION 1 (OF THE MONTH)
A five digit number is formed with the digits 0,1,2,3,4,5 without repition. The probability that it is divisible by 11 is

Answer 1

@mukushla
@lgbasallote
@waterineyes
@walne
@UnkleRhaukus
@satellite73

Answer 2

i think the probability is near to 0.1

Answer 3

For divisible by 11, then difference of Sum of digits at odd places and digits at even places should be 0 or divisible by 11..

For example:

121 : (1 + 1) - (2) = 0

This is the condition to be divisible by 11..

Answer 4

Yes............ I know that @waterineyes
But what about finding the probability




I MAY GIVE YOU OPTIONS :

(a) \(\cfrac{2}{25}\)

(b) \(\cfrac{2}{50}\)

(c) \(\cfrac{3}{50}\)

(d) \(\cfrac{3}{25}\)

Answer 5

Yes.............. @eyust707

Answer 6

So how many of those satisfy waterineyes rule...

Answer 7

@mukushla

Answer 8

i am not going check all of them

Answer 9

well every 11th number is divisible by 11

Answer 10

Yes............... but every 11th number should be that in the series of natural numbers

Answer 11

isnt it a 5 digit no. ?

Answer 12

For making 5 digit number with 0, 1, 2 ,3 4 and 5 find the possible answers first:

First place can be filled with : 5 and other can be filled in 5, 4, 3, 2 etc digits:

So total 5 digit numbers will be:

5*5*4*3*2 = 600 numbers can be formed without repetition..

Answer 13

3/25...i think @vishweshshrimali5

Answer 14

Now check for divisibility..

Answer 15

Why

Answer 16

ahh yes good call waterineyes

Answer 17

@waterineyes how will I check for divisibility

Answer 18

i think the question is for without repetition @waterineyes

Answer 19

Yes........

Answer 20

the greatest number that can be divisible by 11 from rom the digits is 54318 and smallest one is 10241....hence 54318-10241=44077 is the sample space...

Answer 21

ok

Answer 22

yea mitul thats exactly what i was doing...

Answer 23

but that doesn't solve the question

Answer 24

and there will be 4007 numbers...divisible by 11 in this interval....hence probability will be 4007/44077 which is lamost 0.1...and from the options 3/25 is the closest

Answer 25

hes close tho.. you just need to see how many times 11 goes into the lowest one and the highest one

Answer 26

Is it right @vishweshshrimali5

Answer 27

But will all those numbers have the digits 0,1,2,3,4,5

Answer 28

And moreover that approx. part will not work you will have to find out the answer in fractions

Answer 29

that would decrease the toughness of my question...........

Answer 30

but how can a 5-digit number have all 6 numbers....

Answer 31

No only 5 of them

Answer 32

without repetition

Answer 33

then my sample space is correct...

Answer 34

yes

Answer 35

But not sure about the answer

Answer 36

What vish is saying is that some of the 4007 numbers that are divisible by 11 and fall within the sample space may have repetition.

Answer 37

Yes

and also may be that not all those satisfy the given conditions

Answer 38

okk

Answer 39

its tough really....donno....

Answer 40

2/25?

Answer 41

lol...im getting 0.1...and there is not in the options....:D

Answer 42

im also getting 60/600

Answer 43

never mind ... i could be wrong!!

Answer 44

FWIW I did a simulation (attached). I get 0, but I'm not exactly sure why.

Answer 45

answer is 60/600

I used excel to solve it..

Answer 46

I tested it two more ways. I attach one of those. Can someone given an example of a number satisfying the rule.

Answer 47

Because all 3 of my tests show no possibles.

Answer 48

The difference between the sum of the odd numbered digits (1st, 3rd, 5th...) and the sum of the even numbered digits (2nd, 4th...) is divisible by 11.

0,1,2,3,4,5