Answered

Eight cards are marked with the numbers 1,2,3,4,5,6,7,and 8, then shuffled, and three cards are drawn.

A. How many different three-card combinations are possible?

B. How many three-card hands that contain a number less than three?



Answer :

Since3122015
1/2/3, 1/2/4, 1/2/5, 1/2/6, 1/2/7, 1/2/8, 1/3/4, 1/3/5, 1/3/6, 1/3/7, 1/3/8, 1/4/5, 1/4/6, 1/4/7, 1/4/8, 1/5/6, 1/5/7, 1/5/8, 1/6/7, 1/6/8, 1/7/8, 2/3/4, 2/3/5, 2/3/6, 2/3/7, 2/3/8, 2/4/5, 2/4/6, 2/4/7, 2/4/8, 2/5/6, 2/5/7, 2/5/8, 2/6/7, 2/6/8, 2/7/8, 3/4/5, 3/4/6, 3/4/7, 3/4/8, 3/5/6, 3/5/7, 3/5/8, 3/6/7, 3/6/8, 3/7/8, 4/5/6, 4/5/7, 4/5/8, 4/6/7, 4/6/8, 4/7/8, 5/6/7, 5/6/8, 5/7/8, 6/7/8

21 + 15 + 10 + 6 + 3 + 1 = 56

A. 56

B. 46