Question

In a packet there are m different books, n different pens and p different pencils. The number of selections of at least one article of each type from the packet is

• A. $2^{m+n+p}-1$
• B. $(m+1)(n+1)(p+1)-1$
• C. $2^{m+n+p}$
• D. $(2^m-1)(2^n-1)(2^p-1)$

Answer 1

The correct option is D $(2^m-1)(2^n-1)(2^p-1)$

Since each of $(m+n+p)$ items has 2 choices of being selected or not selected; hence total no. of ways of selecting items $=2\times 2\times 2\times 2\times .................(m+n+p)times=2^{m+n+p}$
but one case in this will be when none of the items is selected.
Therefore, no. of ways of selecting at least one item of each type

$(2^m-1)(2^n-1)(2^p-1)$

Hence, option 'D' is correct.