out of 7 gents and 4 ladies a committee of 5 is to be formed. the number of committees such that each committee includes at least one lady is
Answers
1 st ans is wrong right answer is 336
your questions says as at least 3 ladies it means minimum 3 ladies in committee
so we have 4 ladies so 3 or 4 ladies are selecting in committee is valid..
so we have become combination ...
⁸c4×⁴c3 or ⁸c3×⁴c4
(⁸c4×⁴c3) + (⁸c3×⁴c4)
solve it ..
280+56=336
100 percent sure ans...like it..
The number of committees such that each committee includes at least one lady is 441
Given :
Out of 7 gents and 4 ladies a committee of 5 is to be formed
To find :
The number of committees such that each committee includes at least one lady
Solution :
Step 1 of 2 :
Calculate total number of ways of selection
Here it is given that out of 7 gents and 4 ladies a committee of 5 is to be formed
Total number of members = 7 + 4 = 11
Now a committee of 5 is to be formed
∴ Total number of ways of selection
Step 2 of 2 :
Calculate the number of committees such that each committee includes at least one lady
The number of committees such that each committee includes no lady
Hence the number of committees such that each committee includes at least one lady
= 462 - 21
= 441
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