Question:
In how many ways can a committee of $5$ made out $6$ men and $4$ women containing atleast one woman?
In how many ways can a committee of $5$ made out $6$ men and $4$ women containing atleast one woman?
Updated On: Jun 18, 2022
- 246
- 222
- 186
- None of these
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The Correct Option is A
Solution and Explanation
A committee of $5$ out of $6 + 4= 10$ can be
made in $^{10}C_5 = 252$ ways.
If no woman is to be included,
then number of ways $= \,^5C_5$ = 6
$\therefore$ the required number $= 252 -6 = 246$
made in $^{10}C_5 = 252$ ways.
If no woman is to be included,
then number of ways $= \,^5C_5$ = 6
$\therefore$ the required number $= 252 -6 = 246$
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects