is it c? i just try with example

1 vote

The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is

a) 2^n - 1

b) 2^n - 2

c) 2^(n-1) - 1

d) None of these

Please explain your answer.

a) 2^n - 1

b) 2^n - 2

c) 2^(n-1) - 1

d) None of these

Please explain your answer.

2 votes

S(n,2) = 2^(n-1) - 1

http://www.careerbless.com/aptitude/qa/permutations_combinations_imp7.php

Follow this link, to know it in detail.

0

Got it.2^n - 2 ways if the boxes are not identical. But why did you subtract one for identical boxes case.Shouldn't we divide by two for identical boxes case to counter case which now will be similar due to identical boxes.

0

Doubt in a similar question.

How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?

Can we solve it like following?

First, we calculate the no of ways of distributing 5 distinct objects in 3 distinct boxes which are = $3^{5}$ and then we divide it with 3! as we can label the boxes in 3! ways.

Final answer=$3^{5}$ /3!

I know that using the formula of Stirling numbers of the second kind, it can be solved as S(5,1)+S(5,2)+S(5,3). But can the method stated above be used?