A cricket team has 15 members,of whom only 5 | vedclass

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

Question

(C) Total members = $15$,Bowlers = $5$,Non-bowlers = $10$. We need to select $11$ members such that at least $3$ are bowlers.The total number of ways

Vedclass · Accepted Answer

$\frac{12}{13}$

Vedclass · Answer

(C) Total members = $15$,Bowlers = $5$,Non-bowlers = $10$. We need to select $11$ members such that at least $3$ are bowlers.The total number of ways to select $11$ members from $15$ is ${}^{15}C_{11} = {}^{15}C_4 = \frac{15 	imes 14 	imes 13 	imes 12}{4 	imes 3 	imes 2 	imes 1} = 1365$.The number of ways to select at least $3$ bowlers is:Case $1$: $3$ bowlers and $8$ non-bowlers: ${}^5C_3 	imes {}^{10}C_8 = 10 	imes 45 = 450$.Case $2$: $4$ bowlers and $7$ non-bowlers: ${}^5C_4 	imes {}^{10}C_7 = 5 	imes 120 = 600$.Case $3$: $5$ bowlers and $6$ non-bowlers: ${}^5C_5 	imes {}^{10}C_6 = 1 	imes 210 = 210$.Total favorable ways = $450 + 600 + 210 = 1260$.Probability = $\frac{1260}{1365} = \frac{12}{13}$.

$A$ cricket team has $15$ members,of whom only $5$ can bowl. If the names of the $15$ members are put into a hat and $11$ are drawn at random,then the probability of obtaining a team of $11$ containing at least $3$ bowlers is

Similar Questions

An urn contains $25$ balls numbered $1$ to $25$. Suppose an odd number is considered a 'success'. $2$ balls are drawn from the urn with replacement. Find the probability of getting two successes.

The probability that a leap year will have $53$ Fridays or $53$ Saturdays is

$A$ and $B$ are two events such that $P(A) = 0.8$,$P(B) = 0.6$,and $P(A \cap B) = 0.5$. Then the value of $P(A/B)$ is:

For any two independent events $E_1$ and $E_2,$ $P\{(E_1 \cup E_2) \cap (\bar{E}_1 \cap \bar{E}_2)\}$ is

$A$ bag contains $3$ red,$4$ white and $5$ blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

Vedclass Test Series

Exam Paper Generator

Online Exam Module