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Permutation & combination

Questions



Q1. What is the number of ways of selecting four cards from a pack of 52 cards which include exactly 1 red king .

(a) 39200

(b) 39400

(c) 35000

(d) 39280

Solution.a
2C1 x 50C3

= 39200
Solution

Q2. 35Cn+7 = 35C4n-2 Find the value of n .

(a) 3

(b) 6

(c) 4,6

(d) 3,6

Solution. d
(i) n + 7 + 4n - 2 = 35

5n = 30

n = 6

(ii) n + 7 = 4n-2

n = 3
Solution

Q3. nPr = 720nCr Find r .

(a) 7

(b) 6

(c) 3

(d) 8

Solution. b
n!/(n-r)!
= 720 x
n!/r!(n-r)!


r! = 720

r! = 6!

r = 6
Solution

Q4. What is the number of ways of choosing of two black card from a pack of 52 cards .

(a) 333

(b)330

(c) 325

(d) 310

Solution. c
26C2 = 325
Solution

Q5. Ther are n points on a circle . The number of straight line formed by joining them is equal to ?

(a) n

(b) 10

(c) nC2

(d) nP2

Solution.c
nC2

Solution