Permutations And Combination Mcq Model Questions & Answers, Practice Test for ssc chsl tier 1 2024

Question :1

Total number of ways in which six '+' and four '–' sings can be arranged in a line such that no two '–' sings occur together, is

Answer: (c)

First we write six '+' sings at alternate places i.e., by leaving one place vacant between two successive '+' sings.

Now there are 5 places vacant between these sings and these are two places vacant at the ends. If we write 4 '–' sings these 7 places then no two '–' will come together. Hence total number of ways $^7C_4$ = 35

Question :2

In how many different ways can the letters of the word JUDGE be arranged so that the vowels always come together?

Answer: (c)

Reqd. number = 4! × 2! = 24× 2 = 48

Question :3

4 boys and 2 girls are to be seated in a row in such a way that the two girls are always together. In how many different ways can they be seated?

Answer: (d)

Assume the 2 given students to be together (i.e. one).

Now these are five students.

Possible ways of arranging them are = 5! = 120

Now they (two girls) can arrange themselves in 2! ways.

Hence total ways = 120 × 2 = 240

Question :4

Three dice are rolled. The number of possible outcomes in which at least one dice shows 5 is

Answer: (d)

Required number of possible outcomes = Total number of possible outcomes – Number of possible outcomes in which 5 does not appear on any dice. (hence 5 possibilities in each throw)

= $6^3 – 5^3$ = 216 – 125 = 91

Question :5

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

Answer: (c)

Task 1 can not be assigned to either person 1 or 2 i.e. there are 4 options.

Task 2 can be assigned to 3 or 4

So, there are only 2 options for task 2.

So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6.

= 2 × 3 × 4 × 3 × 2 × 1 = 144

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