Ho Search

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

Report Error

View Answer Report Error Discuss

Filed Under: Permutations and Combinations

Q:

A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?

A) 196	B) 186
C) 190	D) 200

Answer & Explanation Answer: B) 186

Explanation:

When at least 2 women are included.

The committee may consist of 3 women, 2 men : It can be done in $4 C_{3} * 6 C_{2}$ ways

or, 4 women, 1 man : It can be done in $4 C_{4} * 6 C_{1}$ ways

or, 2 women, 3 men : It can be done in $4 C_{2} * 6 C_{3}$ ways.

Total number of ways of forming the committees

= $4 C_{2} * 6 C_{3} + 4 C_{3} * 6 C_{2} + 4 C_{4} * 6 C_{1}$

= 6 x 20 + 4 x 15 + 1x 6

= 120 + 60 + 6 =186

Report Error

View Answer Report Error Discuss

Filed Under: Permutations and Combinations

Q:

In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens can be chosen?

A) 180	B) 220
C) 240	D) 160

Answer & Explanation Answer: A) 180

Explanation:

Number of ways of choosing 2 black pens from 5 black pens in $5 C_{2}$ ways.

Number of ways of choosing 2 white pens from 3 white pens in $3 C_{2}$ ways.

Number of ways of choosing 2 red pens from 4 red pens in $4 C_{2}$ ways.

By the Counting Principle, 2 black pens, 2 white pens, and 2 red pens can be chosen in 10 x 3 x 6 =180 ways.

Report Error

View Answer Report Error Discuss

Filed Under: Permutations and Combinations

Q:

12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?

A) 500	B) 490
C) 495	D) 540

Answer & Explanation Answer: C) 495

Explanation:

For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is $12 C_{4}$ = 495.

Therefore, we can draw 495 quadrilaterals

Report Error

View Answer Report Error Discuss

Filed Under: Permutations and Combinations

Q:

How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are to occupy only odd places.

A) 720	B) 576
C) 567	D) 625

Answer & Explanation Answer: B) 576

Explanation:

There are 7 letters in the word Bengali of these 3 are vowels and 4 consonants.

There are 4 odd places and 3 even places. 3 vowels can occupy 4 odd places in $4 P_{3}$ ways and 4 constants can be arranged in $4 P_{4}$ ways.

Number of words = $4 P_{3}$ x $4 P_{4}$ = 24 x 24 = 576

Report Error

View Answer Report Error Discuss

Filed Under: Permutations and Combinations

Q:

How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are never together.

A) 120	B) 640
C) 720	D) 540

Answer & Explanation Answer: C) 720

Explanation:

There are 7 letters in the word ‘Bengali of these 3 are vowels and 4 consonants.

Considering vowels a, e, i as one letter, we can arrange 4+1 letters in 5! ways in each of which vowels are together. These 3 vowels can be arranged among themselves in 3! ways.

Total number of words = 5! x 3!= 120 x 6 = 720

Report Error

View Answer Report Error Discuss

Filed Under: Permutations and Combinations

Q:

In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together ?

A) 18000	B) 17280
C) 17829	D) 18270

Answer & Explanation Answer: B) 17280

Explanation:

Let 4 girls be one unit and now there are 6 units in all.

They can be arranged in 6! ways.

In each of these arrangements 4 girls can be arranged in 4! ways.

Total number of arrangements in which girls are always together = 6! x 4!= 720 x 24 = 17280

Report Error

View Answer Report Error Discuss

Filed Under: Permutations and Combinations

Q:

Mr. and Mrs. Espedido’s property taxes, amounting to $2450, are due on July 1.What amount should the city accept if the taxes are paid eight months in advance and the city can earn 6% compounded monthly on surplus funds?

A) 2354.17	B) 2354
C) 2376	D) 2389

Searching for "Ho"

Quick Links