there are 3 nickles 2 dimes and 5 quarters in a purse. the three coins are selected in succession at random. find the probability of selecting2 nickles , then a quarter.

To find the probability of selecting 2 nickels, then a quarter, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:
We have a total of 10 coins in the purse, and we are selecting 3 coins in succession without replacement. Therefore, the total number of possible outcomes can be calculated using the formula for combinations:

Total possible outcomes = C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Number of favorable outcomes:
We need to select 2 nickels first, and there are only 3 nickels in the purse. So, the number of favorable outcomes for selecting 2 nickels is C(3, 2) = 3! / (2! * (3 - 2)!) = 3.

After selecting 2 nickels, we need to select a quarter. There are 5 quarters in the purse. So, the number of favorable outcomes for selecting a quarter is C(5, 1) = 5.

Therefore, the number of favorable outcomes for selecting 2 nickels, then a quarter is the product of the number of favorable outcomes for each step: 3 * 5 = 15.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Favorable outcomes / Total possible outcomes = 15 / 120 = 1 / 8 = 0.125 = 12.5%

prob = (3/10)(2/9)(5/8) = ....

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