These Permutations And Combinations Class 11 MCQs And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Permutations And Combinations Class 11 MCQs And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Permutations And Combinations Class 11 MCQs

1. In a group containing 6 cows and 4 buffalos, 4 livestock are to be selected in such a way that at least 1 cow should always be present. How many ways of doing that are possible?

(A) 209

(B) 205

(C) 194

(D) 163

**Answer:** 209

2. In how many ways can the letters of the word INDIA be arranged, such that all vowels are never together?

(A) 48

(B) 42

(C) 28

(D) 36

**Answer:** 42

3. In how many ways can the letters of the word ENCYCLOPAEDIA be arranged such that vowels only occupy the even positions?

(A) 453600

(B) 128000

(C) 478200

(D) 635630

**Answer:** 453600

4. There are 35 people in a group. There are 12 school girls, 10 schoolboys, 5 senior citizens, and 8 babies in the group. The organizer of the group wants to select a school girl or a schoolboy as the leader of the group. In how many ways can he do so?

(A) 22

(B) 1/2

(C) 13

(D) 35

**Answer:** 22

5. A bank has 6 digit account number with no repetition of digits within an account number. The first and last digit of the account numbers is fixed to be 4 and 7. How many such account numbers are possible?

(A) 10080

(B) 5040

(C) 890

(D) 1680

**Answer:** 1680

6. A trekking group is to be formed having 6 members. They are to be selected from 3 girls, 4 boys, and 5 teachers. In how many ways can the group be formed so that there are 3 teachers and 3 boys or 2 girls and 4 teachers?

(A) 55

(B) 90

(C) 27

(D) 144

**Answer:** 55

7. In a class, there are 15 students. During a Christmas party, all of them shook hands with each other only once. How many handshakes took place in the class?

(A) 120

(B) 210

(C) 105

(D) 55

**Answer:** 105

8. In how many ways can 4 different balls be distributed among 5 different boxes when any box can have any number of balls?

(A) 5^{4} – 1

(B) 5^{4}

(C) 4^{5} – 1

(D) 4^{5}

**Answer:** 5^{4}

9. The number of combinations of n distinct objects taken r at a time be x is given by

(A) ^{n/2}Cr

(B) ^{n/2}Cr/2

(C) ^{n/2}/2

(D) ^{n}C^{r}

**Answer:** ^{n}C^{r}

10. The value of P(n, n – 1) is

(A) n

(B) 2n

(C) n!

(D) 2n!

**Answer:** n!

11. Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is

(A) 1296

(B) 671

(C) 625

(D) 585

**Answer:** 671

12. There are 12 points in a plane out of which 5 are collinear. The number of triangles formed by the points as vertices is

(A) 185

(B) 210

(C) 220

(D) 175

**Answer:** 210

13. The number of ways of painting the faces of a cube with six different colors is

(A) 1

(B) 6

(C) 6!

(D) None of these

**Answer:** 1

14. If repetition of the digits is allowed, then the number of even natural numbers having three digits is

(A) 250

(B) 350

(C) 450

(D) 550

**Answer:** 450

15. If repetition of the digits is allowed, then the number of even natural numbers having three digits is

(A) 250

(B) 350

(C) 450

(D) 550

**Answer:** 450

16. The number of squares that can be formed on a chessboard is

(A) 64

(B) 160

(C) 224

(D) 204

**Answer:** 204

17. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

(A) 40

(B) 196

(C) 280

(D) 346

**Answer:** 196

18. How many 3-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS if repetition of letters is not allowed

(A) 720

(B) 420

(C) none of these

(D) 5040

**Answer:** 720

19. In how many ways in which 8 students can be sated in a line is

(A) 40230

(B) 40320

(C) 5040

(D) 50400

**Answer:** 40320

20. The number of ways in which 8 distinct toys can be distributed among 5 children is

(A) 5^{8}

(B) 8^{5}

(C) 8_{P5}

(D) 5_{P5}

**Answer:** 5^{8}