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
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The team has atleast one boy
= Total case - No anyone boy
$={ }^{10} C_{4}-{ }^{6} C_{0}$
$=\frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2}-1=210-1 =209$
Was this answer helpful?
0
0
Top Questions on Permutations
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Mathematics
- Permutations
- The rank of the word "TABLE" counted from the rank of the word "BLATE" in dictionary order is:
- AP EAMCET - 2024
- Mathematics
- Permutations
Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to
- MHT CET - 2024
- Mathematics
- Permutations
- The number of ways of distributing \( 500 \) dissimilar boxes equally among \( 50 \) persons is
- MHT CET - 2024
- Mathematics
- Permutations
- 5 books in Math and 3 books in Physics are placed on a shelf so that the books on the same subject always remain together. The possible arrangements are
- JKCET - 2024
- Mathematics
- Permutations
View More Questions
Questions Asked in KEAM exam
Two circles \(C_1\) and \(C_2\) have radii 18 and 12 units, respectively. If an arc of length \( \ell \) of \(C_1\) subtends an angle 80° at the centre, then the angle subtended by an arc of same length \( \ell \) of \(C_2\) at the centre is:
- KEAM - 2024
- Magnitude and Directions of a Vector
- If \( \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x \), where \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
- KEAM - 2024
- Integration
If \( 2 \) is a solution of the inequality \( \frac{x-a}{a-2x}<-3 \), then \( a \) must lie in the interval:
- KEAM - 2024
- Magnitude and Directions of a Vector
- The centre of a square is at the origin of the complex plane. If one of the vertices is at \( -3i \), then the area of the square is:
- KEAM - 2024
- Magnitude and Directions of a Vector
- Number of integers greater than 7000 can be formed using the digits 2, 4, 5, 7, 8 is (Repetition of digits is not allowed):
- KEAM - 2024
- Magnitude and Directions of a Vector
View More Questions
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