Question

Among 15 players, 8 are batsmen and 7 are bowlers. Find the probability that a team is chosen of 6 batsmen and 5 bowlers?
A. \[\dfrac{{}^{8}{{C}_{6}}.{}^{7}{{C}_{5}}}{{}^{15}{{C}_{11}}}\]
B. \[\dfrac{{}^{8}{{C}_{6}}+{}^{7}{{C}_{5}}}{{}^{15}{{C}_{11}}}\]
C. \[\dfrac{15}{28}\]
D. None of these

Answer 1

Hint: We have to find out the probability of choosing a team of 6 batsmen and 5 bowlers. To form the team, we use the formula of probability . the probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.

Complete step by step solution: 
In the question we are given a cricket team which has a
Total number of players equals 15.
Out of the total number of players, 8 of them are batsmen and 7 of them are bowlers.
Now we have to find the probability that a team is chosen of 6 batsmen and 5 bowlers.
and we have to choose a team which consists of a total of 11 players.
Number of ways of choosing 11 players out of 15 players n(S) = \[{}^{15}{{C}_{11}}\]
Let A = event of choosing 6 batsmen of 8 batsmen and 5 bowlers of 7 bowlers.
Then n(A) = \[{}^{8}{{C}_{6}}\times {}^{7}{{C}_{5}}\]
Then put the values in the formula of probability which is the number of favorable outcomes by total number of outcomes.
Therefore, P(A) = \[\dfrac{n(A)}{n(S)}\]
Now put the values in the above equation, we get
\[\dfrac{n(A)}{n(S)}\]= \[\dfrac{{}^{8}{{C}_{6}}\times {}^{7}{{C}_{5}}}{{}^{15}{{C}_{11}}}\]
Thus , the probability of choosing a team of 6 batsmen and 5 bowlers are \[\dfrac{{}^{8}{{C}_{6}}\times {}^{7}{{C}_{5}}}{{}^{15}{{C}_{11}}}\]
Therefore, the correct option is (A).

Note: Students make mistakes because of not reading the requirements which are given in the questions properly. Students must know what the probability is and the formula of probability then they will be able to get the correct answer of the given problem .