euro wrote:Cecilia only remembers that the shipment number comprises 5 digits and the digits 0, 1 and prime numbers do not appear anywhere. She also recalls that there is only one digit that is repeated and it occurs twice in the number. What is the probability that she recalls the shipment number correctly?

(A) 1/24
(B) 3/40
(C) 1/60
(D) 7/90
(E) 1/240


The official answer is [spoiler](E)[/spoiler]

5 numbers need to be chosen from 4,6,8,9 where one of the numbers can repeat.
Let us see how many combinations can be formed.
with 4,6,8,9 for a 5 digit number, we can get 5! combinations out of which 1 number should repeat.
Hence 5!/2! combinations.
=60 combinations.

Now, any of these 4 can repeat. hence, 60*4 = 240 combinations.
Out of these, only 1 will be the shipment number.

Hence probability = 1/240.

Hope this helps!!

kvcpk wrote: Now, any of these 4 can repeat. hence, 60*4 = 240 combinations.
Out of these, only 1 will be the shipment number.

Hope this helps!!

please explain this step , any 4 numbers can be 2 digits
but still not able to understand it.

goyalsau wrote:

kvcpk wrote: Now, any of these 4 can repeat. hence, 60*4 = 240 combinations.
Out of these, only 1 will be the shipment number.

Hope this helps!!

please explain this step , any 4 numbers can be 2 digits
but still not able to understand it.

Let me put it this way.
When '4' repeats, there are 60 possibilities.
When '6' repeats, there are 60 possibilities.
When '8' repeats, there are 60 possibilities.
When '9' repeats, there are 60 possibilities.

Any of these possibilities are possible. Hence we should add them.
60+60+60+60 = 240.

Hope this helps!!

kvcpk wrote: Let me put it this way.
When '4' repeats, there are 60 possibilities.
When '6' repeats, there are 60 possibilities.
When '8' repeats, there are 60 possibilities.
When '9' repeats, there are 60 possibilities.

Any of these possibilities are possible. Hence we should add them.
60+60+60+60 = 240.

Hope this helps!!

I think i got it
we are doing 5!/2! combinations four times.
because there are 4 terms.

thanks for your explanation