by selecting 3 coins, assume that there are 4 dimes, 3 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?

Question

Using Combinations to find the compliment

Answer 1

Hi Brigid,

This is how you go about this.

There are numerous ways of combining the coins to get 25 cents and more. You will end up doing a lot of combinations that might get you confused. What we can do is to find the combination that gives us coins less than 25 cents and subtract it from the total combination for selecting any three (3) coins.

Total for selecting any three coins = 9C3 = 84

Selection of coins that give us less than 25 cents ( (1 dime,2 nickels, & 0 quarters) or ( 0 dime, 3 nickels & 0 quarters)

= 4C1*3C2*2C0 + 4C0*3C3*2C0

= 4(3)(1) + 1(1)(1) = 13

therefore the selection of coins that gives us at least 25cents = 84 -13 =71