Problem
10. 2 different numbers are selected at random from the 16 integers 5 to 20 . (a) Find the number of combinations of selecting 2 different numbers from the 16 integers. (b) Find the number of combinations of selecting 2 different numbers from the multiples of 3 between 5 and 20 . (c) Find the probability that the 2 numbers selected are multiples of 3 .
Solution
Step 1 ：\(\binom{16}{2} = \frac{16 \times 15}{2} = 120\)
Step 2 ：\(\binom{5}{2} = \frac{5 \times 4}{2} = 10\)
Step 3 ：\(\frac{\binom{5}{2}}{\binom{16}{2}} = \frac{10}{120} = \boxed{\frac{1}{12}}\)
