Question

Each of five contestants competing in a quiz are asked 10 quick-fire questions, and their answers may be correct or incorrect with equal probability. The score of each contestant depends on the number of correct answers. What is the probability that

(a) all contestants get a different score?

(b) exactly 2 of them get the same score?

(c) exactly 3 of them get the same score?

Answer 1

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Answer:

(a)

10/10 * 9/10 * 8/10 * 7/10 * 6/10 * 5/10 = 0.1512

(b)

Selecting any two out of 5 and remaining 3 getting different scores from 9, 8 and 7 options

5C2* 10/10 * 1/10 * 9/10*8/10*7/10 = 0.504

(c)

Selecting any three out of 5 and remaining 2 getting different scores from 9 and 8

5C3* 10/10 * 1/10 * 1/10 * 9/10*8/10= 0.072