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A committee of 5 is to be formed out of ...

A committee of 5 is to be formed out of 6 men and 4 ladies. In how many ways can this be done, when
(a) at least 2 ladies are included,
(b) at most 2 ladies are included?

Text Solution

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(i) A committee of 5 persons, consisting of at lest 3 ladies , can be formed in the following ways:
(a) Selecting 3 ladies out of 6 and 2 gents out 8. This can be doen in `""_(6)C_(3) xx ""_(8)C_(2)` ways.
(b) Selecting 4 ladies out of 6 and 1 gent out of 8. This can be done in `""_(6)C_(4)xx ""_(8)C_(1)` ways .
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