Question

If of $p+q+r$ things $p$ are alike, and $q$ be alike, and the rest different, the total number of combinations is

• A. $(p+1)(q+1)r^2-1$
• B. $(p+1)(q+1)r^r-1$
• C. $(p+1)(q+1)2^r+1$
• D. $(p+1)(q+1)2^r-1$

Answer 1

Answer: (D)

$(p+1)(q+1)2^r-1$

No. of combination of $p$ similar object wiil be $(p+1)$

No. of combination of $q$ similar object wiil be $(q+1)$

No. of combination of $r$ different object wiill be $2^r$

Combining all three situation we get $(p+1)(q+1)2^r$

But we have to remove situation where neither of $p,q,r$ occurs and their exist only one situation

So final answer will be $(p+1)(q+1)2^r-1$