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 .

Answer

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Answer

\(\frac{\binom{5}{2}}{\binom{16}{2}} = \frac{10}{120} = \boxed{\frac{1}{12}}\)

Steps

Step 1 ：\(\binom{16}{2} = \frac{16 \times 15}{2} = 120\)

Step 2 ：\(\binom{5}{2} = \frac{5 \times 4}{2} = 10\)

Step 3 ：\(\frac{\binom{5}{2}}{\binom{16}{2}} = \frac{10}{120} = \boxed{\frac{1}{12}}\)