there are three nickels three dimes and four quarters in your pocket. you randomly pick three coin and place them on the counter. the first two coin are a dimes, and the third is quarter

there are three nickels three dimes and four quarters in your pocket. you randomly pick three coin and place them on the counter. the first two coin are a dimes, and the third is quarter

Probatitly of what happening?

To solve this problem, we need to determine the probability of picking two dimes and one quarter from the given set of coins in your pocket.

First, let's find the total number of ways we can pick three coins.
Since we have three nickels, three dimes, and four quarters, the total number of coins is 3 + 3 + 4 = 10. Therefore, there are 10C3 ways to select three coins out of the ten.

10C3 = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.

Now, let's determine the number of ways to pick two dimes and one quarter.
The number of ways we can select two dimes from the three available is 3C2 = 3.
Similarly, the number of ways to select one quarter from the four available is 4C1 = 4.

To find the total number of ways to pick two dimes and one quarter, we multiply these two values: 3 * 4 = 12.

Now, we can find the probability by dividing the number of successful outcomes (selecting two dimes and one quarter) by the total number of outcomes (selecting any three coins):
Probability = Number of successful outcomes / Total number of outcomes
= 12 / 120
= 1 / 10
= 0.1
= 10%.

Therefore, the probability of randomly picking two dimes and one quarter from your pocket is 10%.