## Chapter 7 Permutations and Combinations

Q1. **The value of P(n, n-1) is**

a. n

b. n!

c. 2n

c. 2n!

Answer: **(b) n!**

**Q2. The number of ways in which 8 students can be seated in a line is**

a. 5040

b. 50400

c. 40230

d. 40320

Answer: (d) 40320

Q3. **The number of ways 4 boys and 3 girls can be seated in a row so that they are alternate is**

a. 12

b. 104

c. 144

d. 256

Answer: **(c) 144**

Q4. **A coin is tossed n times, the number of all the possible outcomes is**

a. 2n

b. 2^{n}

c. C(n, 2)

d. P(n, 2)

Answer: **(b) 2 ^{n}**

Q5. **There are 10 true-false questions in an examination. These questions can be answered in:**

a. 20 ways

b. 100 ways

c. 512 ways

d. 1024 ways

Answer: **(d) 1024 ways**

Q6. **In how many ways can we paint the six faces of a cube with six different colours?**

a. 30

b. 6

c. 6!

d. None of the above

Answer: **(a) 30**

Q7. 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: (b) 210

Q8. 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: (b) 671

Q9. 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: (c) 450

Q10. The number of ways can the letters of the word ASSASSINATION be arranged so that all the S are together is

(a) 152100

(b) 1512

(c) 15120

(d) 151200

Answer: (d) 151200