A group of students comprises 5 boys and n gi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Total students = $5 + n$.We need to select $3$ students such that there is at least one boy and at least one girl.The possible cases are:Case $1$:

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(D) Total students = $5 + n$.We need to select $3$ students such that there is at least one boy and at least one girl.The possible cases are:Case $1$: $1$ boy and $2$ girls: $^5C_1 	imes ^nC_2 = 5 	imes \frac{n(n-1)}{2} = \frac{5n(n-1)}{2}$.Case $2$: $2$ boys and $1$ girl: $^5C_2 	imes ^nC_1 = 10 	imes n = 10n$.Sum of ways = $\frac{5n(n-1)}{2} + 10n = 1750$.Multiply by $2$: $5n(n-1) + 20n = 3500$.Divide by $5$: $n(n-1) + 4n = 700$.$n^2 - n + 4n = 700 \Rightarrow n^2 + 3n - 700 = 0$.Solving the quadratic equation: $(n + 28)(n - 25) = 0$.Since $n$ must be positive,$n = 25$.

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways,in which a team of $3$ students can be randomly selected from this group such that there is at least one boy and at least one girl in each team,is $1750$,then $n$ is equal to

Similar Questions

The number of non-negative integer solutions of the equations $6x + 4y + z = 200$ and $x + y + z = 100$ is

The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

Out of all possible $8$-digit numbers formed using all the digits $0, 0, 1, 1, 2, 3, 4, 4$,a number is randomly selected. The probability that the selected number is odd is:

In an examination,there are $3$ multiple-choice questions,and each question has $4$ choices. The number of ways in which a student can fail to get all answers correct is:

If $\frac{{}^{n + 2}C_6}{{}^{n - 2}P_2} = 11$,then $n$ satisfies the equation

Vedclass Test Series

Exam Paper Generator

Online Exam Module