# Two cards are drawn together from a pack of 52 cards. The probability that one is a club and one is a diamond ?

Two cards are drawn together from a pack of 52 cards. The probability that one is a club and one is a diamond ?

A. 13/51

B. 1/52

C. 13/102

D. 1/26

### **Answer : ** C. 13/102...

## Explanation:

n(S) = Total number of ways of drawing 2 cards from 52 cards = 52C2.

Let E = event of getting 1 club and 1 diamond.

We know that there are 13 clubs and 13 diamonds in the total 52 cards.

Hence, n(E) = Number of ways of drawing one club from 13 and one diamond from 13 = ^{13}C_{1} × ^{13}C_{1} = 13/102

P(E) = n(E)/n(S)

= (^{13}C_{1} × ^{13}C_{1}) / ^{52}C_{2}

= 13/102.