1. Three coins are tossed. What is the probability of getting exactly two tails?

A.1/4
B.3/8
C.1/2
D.5/8
E. None of these

Option “B” is correct.

Total event=(HHH, HHT, HTH, THH, THT, HTT, TTH, TTT)

=8

Possible ways =(THT, HTT, TTH)=3

Required probability=3/8

2. A dice is rolled, what is the probability of the outcome is a prime number?

A. 1/2
B. 2/3
C. 5/6
D. 1/3
E. None of these

Option “A” is correct.

Total event=(1, 2, 3, 4, 5, 6)

Possibility of getting Prime number=(2, 3, 5)

Required probability=3/6=1/2
3. Two cards are drawn at the random from a pack of cards. What is the probability that both are Kings?

A. 3/221
B. 4/221
C. 5/221
D. 1/221
E. None of these

Option “D” is correct.

The number of kings in the pack=4

Total number of cards=52

Required probability=4C2 /52C2 = (4 * 3)/(52 * 51)

=1/221
4. A bag contains 3 red balls and 4 green balls. What is the probability of selecting 2 green balls from the bag?

A. 1/7
B. 2/7
C. 3/7
D. 4/7
E. None of these

Option “B” is correct.

Required probability=4C2/7C2

= (4 * 3)/(7 * 6)

=2/7
5. What is the probability of selecting 2 blue balls from a bag containing 4 red balls and 5 blue balls?

A. 5/18
B. 7/18
C. 1/3
D. 2/9
E. 3/7

Option “A” is correct.

Required probability=5C2 / 9C2  

= 20/72

= 5/18
6. In how many ways the letters of the word ‘ARMOUR’ can be arranged?

A. 720
B. 360
C. 120
D. 650
E. None of These

Option “B” is correct.

Total letters = 6,

but R has come twice.

Number of arrangements = 6!/2! = (6 * 5 * 4 * 3 * 2 * 1)/(2 * 1) = 360
7. In how many ways the letters of the word “COURSE”can be arranged?

A. 360
B. 240
C. 540
D. 128
E. None of these

Option “E” is correct.
Required ways=6!=720
8. In how many ways the letters of word “SIMPLE” can be arranged so that all vowels come together?

A. 180
B. 210
C. 240
D. 270
E. 120

Option “C” is correct.

Total letters = 6

Vowels = I, E = 2

Required ways = 2! * 5!

= 240
9. How many ways the letters of the word “CURRENT” be arranged?

A. 2520
B. 1260
C. 5040
D. 720
E. None of these

Option “A” is correct.
Required ways = 7!/2! = 2520
10. How many different ways can the word “YUMMY” be arranged?

A. 90
B. 24
C. 120
D. 60
E. 30

Option “E” is correct.
Required number of ways = 5!/(2!2!) = 30
Pages: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

157 thoughts on “Probability and Permutation and Combination”

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