1. ## Coin problem

Ayushi has six coins with a total value of 30 cents. The coins are not all the same.
Two of Ayushi’s coins will be chosen at random. What is the probability that the
total value of the two coins will be less than 15 cents? Express your answer as a
common fraction.

2. Hello, sri340!

Ayushi has six coins with a total value of 30 cents.
The coins are not all the same.

Two of her coins will be chosen at random.
What is the probability that the total value of the two coins will be less than 15 cents?
The only way to have 6 coins worth 30¢ is: 5 pennies and 1 quarter.

There are: . ${6\choose2} \,=\,15$ possible outcomes.

To have less than 15¢, we must draw two pennies.
. . There are: . ${5\choose2} \,=\,10$ ways.

Therefore: . $P(< 15\rlap{/}c) \:=\:\frac{10}{15} \;=\;\frac{2}{3}$