Discrete Math Question

Question

Suppose that there are 13 cards, numbered 1,2,......, 13. A hand is 5 cards, the order in which the cards are dealt not making any difference. How many hands are there? The value of a hand, v(hand), is the sum of the numbers of the cards in the hand. What is the smallest possible value of a hand? What is the largest? How many hands have a value of 20? What is the average value of a hand? (want the exact average value). What do you think is the single most common value of a hand?

Answer 1

13!/8!/3!= 13x12x11x10x9/3x2

13,12,11,10,9

13,12,11,10,8

13,12,11,10,7

...

13,4,3,2,1

...

5,4,3,2,1

13x12x11x10,x9

smallest=1+2+3+4+5=15

largest: 13+12+11+10+9= 55

10+4+3+2+1=20

9+5+3+2+1=20

8+6+3+2+1=20

average = (15+55)/2 =35