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 …………

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 6860.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

case	7 red applies	5 white apples	8 oranges	Selection of 5 fruits
I	1	1	3	$^{7} C_{1} \cdot^{5} C_{1} \cdot^{8} C_{3}$
II	1	2	2	$^{7} C_{1} \cdot \cdot^{5} C_{2} \cdot^{8} C_{2}$
III	2	1	2	$^{7} C_{2} \cdot^{5} C_{1} \cdot^{8} C_{2}$

Total number of ways =
$\begin{array}{l} =^{7} C_{1} \cdot^{5} C_{1} \cdot^{8} C_{3} +^{7} C_{1} \cdot^{5} C_{2} \cdot^{8} C_{2} +^{7} C_{2} \cdot^{5} C_{1} \cdot^{8} C_{2} \\ = 7.5 \cdot 56 + 7 \cdot 10.28 + 21.5 \cdot 28 \\ = 7.5 \cdot 28 (2 + 2 + 3) \\ = 7 \times 5 \times 28 \times 7 = 6860 \end{array}$