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


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

Sol. The two digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5 without repeating digits are as follows :

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 }
n (S) = 25
P is the event that number so formed is even
P = { 10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54 }
∴  n (P) = 13
Q is the event that number so formed is divisible by 3
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
R = { 51, 52, 53, 54 }

 n (R) = 4

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