SOLUTION: a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket-keepers.in how many ways you can do it so that the team contain at least 3 bowlers and 1 wicket-keeper

Question 1024550: a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket-keepers.in how many ways you can do it so that the team contain at least 3 bowlers and 1 wicket-keeper?
(a) 2472
(b) 960
(c) 840
(d) 420
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
a cricket team of first 11 players out of 16 including 4 bowlers
and 2 wicket-keepers.in how many ways you can do it so that the
team contain at least 3 bowlers and 1 wicket-keeper?

Do you mean:

1.  "the team contain at least 3 bowlers and AT LEAST 1 
wicket-keeper"?
 
or do you mean:

2.  "the team contain at least 3 bowlers and EXACTLY 1 
wicket-keeper"? 

----------------

I'll do them both.

There are:

 4 bowlers
 2 wicket-keepers
10 non-bowlers-not-wicket keepers.

Case A.  There are exactly 3 bowlers, exactly 1 wicket 
keeper, and 7 non-bowlers-non-wicket-keepers.

(4C3)(2C1)(10C7) = 960
 
Case B.  There are exactly 3 bowlers, exactly 2 wicket
keepers, and 6 non-bowler-non-wicket-keepers.

(4C3)(2C2)(10C6) = 840

Case C.  There are exactly 4 bowlers, exactly 1 wicket
keepers, and 6 non-bowler-non-wicket-keepers.

(4C4)(2C1)(10C6) = 420

Case D.  There are exactly 4 bowlers, exactly 2 wicket
keepers, and 5 non-bowler-non-wicket-keepers.

(4C4)(2C2)(10C5) = 252

Answer: 960+840+420+252 = 2472, that's choice (a).

------------------------

Considering it to be the other way where there is 
exactly 1 wicket-keeper, we omit cases B and D.

Answer: 960+420 = 1380, that's not a choice so it 
must have meant AT LEAST 1 wicket-keepers.

Edwin

RELATED QUESTIONS
you are selecting a cricket team of first 11 players out of 16 including 4 bowlers and... (answered by Edwin McCravy)

Among 18 members of a cricket club there are 2 wicket keepers and 5 bowlers.in how many... (answered by Boreal)

1)Amoung 18 members of a cricket club, there are 2 wicket keepers, 5 bowlers and 6... (answered by stanbon)

indian cricket team consist of 16 members. it includes 2 wicket keeper and 5 bowlers.the... (answered by stanbon)

Here is the problem: A soccer team has 16 players. How many ways can the coach choose a... (answered by rothauserc,Edwin McCravy)

in how many ways can a team of 11 players be selected from 13 boys (answered by ikleyn,santibanezkrissy)

Out of 16 players a team of 11 players is to be selected how many teams can be formed if (answered by fractalier)

In how many ways can a coach select 5 players from a team of 10... (answered by stanbon)

1. Suppose 40 out of 90 people re bowlers and 3 out of every 16 of the bowlers have their (answered by macston)