Test Preparation on Permutation and Combination For Competitive Exam

1.

How many 3 digit number can be formed with the digits 5, 6, 2, 3, 7 and 9 which are divisible by 5 and none of its digit is repeated?

first two places can be filled in 5 and 4 ways respectively so, total number of 3 digit number = 5*4*1 = 20

2.

In how many different ways can the letter of the word ELEPHANT be arranged so that vowels always occur together?

Vowels = E, E and A. They can be arranged in 3!/2! Ways so total ways = 6!*(3!/2!) = 2160

3.

There are 4 bananas, 7 apples and 6 mangoes in a fruit basket. In how many ways can a person make a selection of fruits from the basket.

Zero or more bananas can be selected in 4 + 1 = 5 ways (0 orange, 1 orange, 2 orange, 3 orange and 4 orange) similarly apples can be selected in 7 +1 = 8 ways and mangoes in 6 +1 = 7 ways so total number of ways = 5*8*7 = 280 but we included a case of 0 orange, 0 apple and 0 mangoes, so we have to subtract this, so 280-1=279 ways

4.

There are 15 points in a plane out of which 6 are collinear. Find the number of lines that can be formed from 15 points.

From 15 points number of lines formed = 15c2 6 points are collinear, number of lines formed by these = 6c2 So total lines = 15c2 – 6c2 + 1 = 91

5.

In how many ways 4 Indians, 5 Africans and 7 Japanese be seated in a row so that all person of same nationality sits together

4 Indians can be seated together in 4! Ways, similarly for Africans and Japanese in 5! and 7! respectively. So total ways = 4! 5! 7! 3!

6.

In how many ways 5 Americans and 5 Indians be seated along a circular table, so that they are seated in alternative positions

First Indians can be seated along the circular table in 4! Ways and now Americans can be seated in 5! Ways. So 4! 5! Ways

7.

4 matches are to be played in a chess tournament. In how many ways can result be decided?

Every chess match can have three result i.e. win, loss and draw so now of ways = 3*3*3*3 = 81 ways

8.

There are 6 players in a cricket which is to be sent to Australian tour. The total number of members is 12. If 2 particular member is always included

only 4 players to select, so it can be done in 10c4 = 210

9.

If 3 particular player is always excluded

6 players to be selected from remaining 9 players in 9c6 = 84 ways

10.

In a group of 6 boys and 5 girls, 5 students have to be selected. In how many ways it can be done so that at least 2 boys are included

6c2*5c3 + 6c3*5c2 + 6c4*5c1 + 6c5


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