Write S, n(S) and events A, B, C: Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition. A: number is even. B: number is divisible by 3. C: number is greater than 50.

Write sample space 'S' and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).

(4) Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits.
Condition for event A : The number formed is even
Condition for event B : The number formed is divisible by 3.
Condition for event C : The number formed is greater than 50.

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Answer: n(S) = 25; n(A) = 13; n(B) = 9; n(C) = 4

The tens digit cannot be 0, so it is one of 1 to 5 (5 ways), and the units digit is any of the other 5 digits: \(5 \times 5 = 25\).

S = {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43, 45, 50, 51, 52, 53, 54}

A (units digit 0, 2 or 4) = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}, n(A) = 13

B (digit sum divisible by 3) = {12, 15, 21, 24, 30, 42, 45, 51, 54}, n(B) = 9

C = {51, 52, 53, 54}, n(C) = 4

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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Write S, n(S) and events A, B, C: Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition. A: number is even. B: number is divisible by 3. C: number is greater than 50.

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