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

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

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