1. Tardigrade
  2. Question
  3. Mathematics
  4. Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$ oranges. If in the selected $5$ fruits, at least $2$ oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer $5 $ fruits to Anil is______

JEE MainJEE Main 2023Permutations and Combinations

Solution:

$7$ Red apple(RA),5 white apple(WA), 8 oranges $( O )$
5 fruits to be selected (Note:- fruits taken different)
Possible selections :- $(2 O , 1 RA , 2 WA )$ or $(2 O$,
$2 RA , 1 WA )$ or $(3 O , 1 RA , 1 WA )$
$\Rightarrow{ }^8 C _2{ }^7 C _1{ }^5 C _2+{ }^8 C _2{ }^7 C _2{ }^5 C _1+{ }^8 C _3{ }^7 C _1{ }^5 C _1 $
$ \Rightarrow 1960+2940+1960$
$ \Rightarrow 6860$