Question:
In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
Updated On: Jun 7, 2024
- 159
- 209
- 200
- 240
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The Correct Option is B
Solution and Explanation
The team has atleast one boy
= Total case - No anyone boy
$={ }^{10} C_{4}-{ }^{6} C_{0}$
$=\frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2}-1=210-1 =209$
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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