14 How many ways are there to put 5 balls in 2 boxes if a th

14. How many ways are there to put 5 balls in 2 boxes if

(a) the balls are distinguishable and the boxes are distinguishable?

(b) the balls are distinguishable and the boxes are not?

(d) the balls are not distinguishable and neither are the boxes?

15. How many ways are there to put 4 balls in 3 boxes if

(a) the balls are distinguishable and the boxes are distinguishable?

(b) the balls are distinguishable and the boxes are not?

(d) the balls are not distinguishable and neither are the boxes?

16. Suppose a poker hand has seven cards instead of five. Compute the probabilities of the following poker hands:

(a) a seven-card straight.

(b) a four cards of one rank and three cards of a different rank.

(d) two cards of each of three different ranks, and a card of a fourth rank.

(e) three cards of one rank and four cards of each of four different ranks.

(f) seven cards each of different rank.

a)u can select the distuishable as 5C2 becuase we can make difference.

b)if the boxes are not distinguishable it will be considered as only one option no matter how many boxes are there.

so the question will become 5 balls in 1 box

and the answer will be 5C1 =5

C) now the balls are not distinguisable therefore they will become as 1 choice and box are 2

therefore ways will be 2C1=2

d)now the box and balls are both not distinguishable therefore both will be counted as 1

and the answer will be 1

(d) the balls are not distinguishable and neither are the boxes?