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(A) We have $7$ red apples $(RA)$,$5$ white apples $(WA)$,and $8$ oranges $(O)$. We need to select $5$ fruits such that there are at least $2$ oranges

Vedclass · Accepted Answer

$6860$

Vedclass · Answer

(A) We have $7$ red apples $(RA)$,$5$ white apples $(WA)$,and $8$ oranges $(O)$. We need to select $5$ fruits such that there are at least $2$ oranges,at least $1$ red apple,and at least $1$ white apple.The possible combinations $(O, RA, WA)$ are:$1. (2, 1, 2) \Rightarrow {}^{8}C_{2} 	imes {}^{7}C_{1} 	imes {}^{5}C_{2} = 28 	imes 7 	imes 10 = 1960$$2. (2, 2, 1) \Rightarrow {}^{8}C_{2} 	imes {}^{7}C_{2} 	imes {}^{5}C_{1} = 28 	imes 21 	imes 5 = 2940$$3. (3, 1, 1) \Rightarrow {}^{8}C_{3} 	imes {}^{7}C_{1} 	imes {}^{5}C_{1} = 56 	imes 7 	imes 5 = 1960$Total number of ways = $1960 + 2940 + 1960 = 6860$.

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