Hello, Jon!

Here are a few of them . . .

1) What is the probability of drawingexactly2 red cards

in a hand of 3 cards drawn from a deck of 52 cards?

There are: . possible outcomes.

We want two Reds and one Black.

. . There are: . ways.

Therefore: .

2) State the coefficient of the term containing in the expansion of

In the expansion of , the only term with is:

. . .

3) A coin is tossed 20 times in a row.

The probability of exactly heads occurring is given by the term containing

in the binomial expansion of , where

Calculate the probability that exactly 9 heads will be tossed.

We have: .

We want the term with

There are three cases . . .4) A bag contains 12 blocks: 5 red, 4 blue, and 3 green.

If 7 blocks are selected randomly, determine the number of ways

thatat least2 blocks of each color are drawn.

. . (1) {RR|BB|GGG}: . ways.

. . (2) {RR|BBB|GG}: . ways.

. . (3) {RRR|BB|GG}: . ways.

Therefore, there are: . ways.