# Probability and Permutation and Combination

 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 theseOption “B” is correct.Total event=(HHH, HHT, HTH, THH, THT, HTT, TTH, TTT)=8Possible ways =(THT, HTT, TTH)=3Required 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 theseOption “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 theseOption “D” is correct.The number of kings in the pack=4Total number of cards=52Required 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 theseOption “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. 3/7Option “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 TheseOption “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 theseOption “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. 120Option “C” is correct.Total letters = 6Vowels = I, E = 2Required 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 theseOption “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. 30Option “E” is correct. Required number of ways = 5!/(2!2!) = 30
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