Question

A Cricket team squad has 15 members. In
how many ways a team of 11 members can
be selected such that one of the players in
the squad is injured hence he cannot be
selected and one of the players is a captain
hence he has to be in every team?
Select one:
¹³ C¹⁰
¹⁴C¹¹
¹¹C¹⁰
¹³C¹¹​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

• A Cricket team squad has 15 members

• A team of 11 members can be selected such that one of the players in the squad is injured hence he cannot be selected

• Also one of the players is a captain hence he has to be in every team

TO DETERMINE

The number of selection

CALCULATION

The total number of members in the Cricket team squad = 15

Now one of the players in the squad is injured

So he cannot be selected

Therefore the remaining number of members in the Cricket team squad = 15 - 1 = 14

Also one of the players is a captain

So he ( Captain ) has to be in every team

Therefore we have to select ( 11 - 1 ) = 10 members from 14 - 1 = 13 members in the Cricket team squad

This selection can be done in $\sf{\large{ {}^{13} C_{10}}} \: \: \: ways$

Hence the required answer is $= \sf{\large{ {}^{13} C_{10}}} \: \: \:$

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Answer 2

Step-by-step explanation:

\displaystyle\huge\red{\underline{\underline{Solution}}}

Solution

GIVEN

A Cricket team squad has 15 members

A team of 11 members can be selected such that one of the players in the squad is injured hence he cannot be selected

Also one of the players is a captain hence he has to be in every team

TO DETERMINE

The number of selection

CALCULATION

The total number of members in the Cricket team squad = 15

Now one of the players in the squad is injured

So he cannot be selected

Therefore the remaining number of members in the Cricket team squad = 15 - 1 = 14

Also one of the players is a captain

So he ( Captain ) has to be in every team

Therefore we have to select ( 11 - 1 ) = 10 members from 14 - 1 = 13 members in the Cricket team squad

This selection can be done in \sf{\large{ {}^{13} C_{10}}} \: \: \: ways

13

C

10

ways

Hence the required answer is = \sf{\large{ {}^{13} C_{10}}} \: \: \:=

13

C

10

━━━━━━━━━━━━━━━━

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Find the probability of a 10 year flood occurring at least once in the next 5 years is

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