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Q:

There are 7 men and 10 women on a committee selection pool.A committee consisting of President,Vice-President, and Treasurer is to be formed.How many ways can exactly two men be on the committe ?

A) 1200	B) 1240
C) 1260	D) 1620

Answer & Explanation Answer: C) 1260

Explanation:

There are $7 C_{2}$ ways of selecting two men, and $10 C_{1}$ ways of selecting a woman.Since each position in the committee is different,arrange the three people in 3! ways.

So, $7 C_{2} * 10 C_{1} * 3! = 1260$

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Q:

A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls.How many councils can have Jason on the council?

A) 715	B) 725
C) 419	D) 341

Answer & Explanation Answer: A) 715

Explanation:

If Jason is on th ecouncil,this reduces the selction pool to only 13 people,out of which we still need to select 4.

So, $13 C_{4}$ = 715

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Q:

How many ways can you select 17 songs for mix CD out of possible 38 songs?

A) 2878	B) 2878 x 10^2
C) 290183753	D) 2878 x 10^10

Answer & Explanation Answer: D) 2878 x 10^10

Explanation:

since it is a combination = $38 C_{17}$ = 2878 x 10^10

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Q:

There are 6 bowlers and 9 batsmen in a cricket club. In how many ways can a team of 11 be selected so that the team contains at least 4 bowlers?

A) 1170	B) 1200
C) 720	D) 360

Answer & Explanation Answer: A) 1170

Explanation:

Possibilities Bowlers Batsmen Number of ways

6 9

1 4 7 $(6 C_{4} * 9 C_{7})$

2 5 6 $(6 C_{5} * 9 C_{6})$

3 6 5 $(6 C_{6} * 9 C_{5})$

$(6 C_{4} * 9 C_{7})$ = 15 x 36 = 540

$(6 C_{5} * 9 C_{6})$ = 6 x 84 = 504

$(6 C_{6} * 9 C_{5})$ = 1 x 126 = 126

Total = 1170

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Q:

In how many ways, can zero or more letters be selected form the letters AAAAA?

A) 5	B) 6
C) 2	D) 8

Answer & Explanation Answer: B) 6

Explanation:

Selecting zero'A's= 1

Selecting one 'A's = 1

Selecting two 'A's = 1

Selecting three 'A's = 1

Selecting four 'A's = 1

Selecting five 'A's = 1

=> Required number ofways =6

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Q:

How many ways are there to select a subcommittee of 7 members from among a committee of 17?

A) 19000	B) 19448
C) 19821	D) 19340

Answer & Explanation Answer: B) 19448

Explanation:

Since it does not matter what order the committee members are chosen in, the combination formula is used.

Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.

C(17,7)= 19,448

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Q:

The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we have to select 1 wicket keeper and atleast 4 bowlers?

A) 1024	B) 1900
C) 2000	D) 1092

Answer & Explanation Answer: D) 1092

Explanation:

We are to choose 11 players including 1 wicket keeper and 4 bowlers or, 1 wicket keeper and 5 bowlers.

Number of ways of selecting 1 wicket keeper, 4 bowlers and 6 other players in $2 C_{1} * 5 C_{4} * 9 C_{6}$ = 840

Number of ways of selecting 1 wicket keeper, 5 bowlers and 5 other players in $2 C_{1} * 5 C_{5} * 9 C_{5}$ =252

Total number of ways of selecting the team = 840 + 252 = 1092

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Q:

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

A) 209	B) 290
C) 200	D) 208

Answer & Explanation Answer: A) 209

Explanation:

We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

Required number of ways = $(6 C_{1} * 4 C_{3}) + (6 C_{2} * 4 C_{2}) + (6 C_{3} * 4 C_{1}) + 6 C_{4}$

= $(6 C_{1} * 4 C_{1}) + (6 C_{2} * 4 C_{2}) + (6 C_{3} * 4 C_{1}) + 6 C_{2}$ = 209.

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Filed Under: Permutations and Combinations

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