# math

posted by .

Three coins are selected from 10 coins: 4 dimes, 4 nickels, and 2 quarters.

In how many possible ways can the selection be made so that the value of the coins is at least 25 cents?

I know that the total outcomes equals 120, but how do I find how many of these have the value of at least 25 cents?

• math -

The answer is 92. Anyone have idea how to solve this or why the answer is 92? Thanks in advance!

• math -

Consider the cases which do not add up to 25, they would be
DNN and NNN
DNN -- C(4,1)C(4,2) = 24
NNN -- C(4,3 = 4
so 28 cases are not allowed
leaving 120 - 28 = 92

another way:

You have to list the possible outcomes , then evaluate each one, finally add up the allowable cases

QQQ - C(4,1) = 4
QQD - C(2,2)C(4,1) = 4
QNN - C(2,1)C(4,2) = 12
QDD - .... = 12
QND - .... = 32
DDD - .... = 4
DDN - .... = 24
DNN gives us < 25 cents
NNN gives us < 25 cents.

the total of the above is 92

## Similar Questions

1. ### math

Jo has 37 coins (all nickels, dimes and quarters) worth \$5.50. She has 4 more quarters than nickels. How many of each type of coins does she have?
2. ### Math problem I need help with

Combination of coins that can be used; fifty-cent piece, quarters, dimes, nickels, and pennies Q: My 3 types of coins total 37 cents. I have fewer than 4, but more than 1, of each coin. What are the coins?
3. ### Math

Shirley has 18 coins. One sixth of the coins are quarters, one third of the coins are dimes, and one half of the coins are nickels. What is the value of Shirley's coins?
4. ### math

selecting three (3) coins, but assume that there are 5 dimes, 4 nickels, and 2 quarters. In how many possible ways can the selection be made so that the value of the coins is at least 25 cents?
5. ### Math

Select three (3) coins, but assume that there are 4 dimes, 4 nickels, and 2 quarters. In how many possible ways can the selection be made so that the value of the coins is at least 25 cents?
6. ### Math

Assume that you have 7 dimes and 5 quarters (all distinct), and you select 4 coins. In how many ways can the selection be made so that at least 3 coins are dimes?