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Out of 8 gentlemen and 5 ladies a committee of 5 is to be formed. Find the number of ways in which this can be done so as to include atleast 2 ladies.

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Detailed Solution

The selection of committee can be done as follows:

S.No	No. of gentle men	No. of ladies	No. of ways to select committee
1	3	2	$^{8} C_{3} \times^{5} C_{2} = 560$
2	2	3	$^{8} C_{2} \times^{5} C_{3} = 280$
3	1	4	$^{8} C_{1} \times^{5} C_{4} = 40$
4	0	5	$^{8} C_{0} \times^{5} C_{5} = 1$

Total number of committees = 560 + 280 + 40 + 1 = 881

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