Question

How many different cricket teams of 11 players can be selected from 14 cricket players of which
only two can play as wicketkeeper? Given each team must have exactly one wicketkeeper?
(a) 130
(b) 132
(c) 140
(d) None of these


solve with correct solution ​

Answer 1

Answer:

There are 15 players for selection. Lets assume that all players are allrounders. player A is always selected, therefore there will be only 10 players to be selected. Again one particular player B cant be selected, so there are 13 players from which you are gonna select 10 players.

So according to permutation and combination theorems that will be 13 C 10 i. e fact(13)/(fact(10)*fact(3))= 286 ways.

But if you consider real scenario:

There will be 3 opening batsmen.

There will be 5 batsmen in which two are wicket keeper.

2 All-rounders(one fast bowling and another spin bowling)

4 fast bowlers

One spinner

So in the above mentioned scenario, spinner is selected who is player A in above mentioned para. So, now according to pitches one all-rounder will be selected. And from 4 fast bowlers, 3 will be selected. From 3 opening batsmen, 2 will be selected. In 5 batsmen one keper batsmen is eliminated, who is player B.

So, no. of ways will be

3C2*4C4*2C1*4C3= 24 ways

Hope this helps you☺

Answer 2

Answer:

the answer of the question is 132