Question

Form two digit numbers using the digit 0,1,2,3,4,5 without repeating the digits.
P is the event that the number so formed is even:
Q is the even that the number so formed is divisible by 3.
R is the even that the number so formed is greater than 50.

Answer 1

Two-digit numbers are formed using the digits 0, 1, 2, 3, 4 and 5 (without repeating the digits).
We have:
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}
Or,
n(S) = 25

Now,
P is the event that the number so formed is even.
Thus, we have:
P = {10, 12,14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}
∴ n(P) = 13

Q is the event that the number so formed is divisible by 3.
Thus, we have:
Q = {12, 15, 21, 24, 30, 42, 45, 51, 54}
∴ n(Q) = 9

R is the event that the number so formed is greater than 50.
Thus, we have:
R = {51, 52, 53, 54}
∴ n(R) = 4