Question

There are 5 mangoes and 4 apples. In how many different ways can a selection of fruits be made if
(i) fruits of the same kind are different
(ii) fruits of the same kind are identical?

Answer 1

i. If fruits are different,

Total no. of fruits $=5+4=9$

No. of ways of selecting one or more fruit $=2^9-1=511$

ii. If fruits of same kind are identical,

No. of ways of selecting mango $={}^5{C}_n$

No. of ways of selecting apples $={}^4{C}_n$

No. of ways of selecting at least one or more mango $=2^5-1=31$

No. of ways of selecting at least one or more apples $=2^4-1=15$

$\therefore$ No. of ways $=31+15=46$

Hence, solved.