Question

Supposed repetition are not allowed.
a) How many three-digit numbers can be formed from the six digits 2, 3, 5, 6, 7 and 9?
b) How many are less than 500? [2]
c) How many are even? [2]
3.2 Simplify
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Answer 1

a) There are six digits 2, 3, 5, 6, 7 and 9. Supposed repetition are not allowed.

Then

$$P(6,3)=\dfrac{6!}{(6-3)!}=6(5)(4)=120$$

120 three-digit numbers can be formed.

(b)

Digit 2 is at the first place

$$P(5,2)=\dfrac{5!}{(5-2)!}=5(4)=20$$

Digit 3 is at the first place

$$P(5,2)=\dfrac{5!}{(5-2)!}=5(4)=20$$

$$20+20=40$$

40 three-digit numbers less 500 can be formed.

(c) Digit 2 is at the third place

$$P(5,2)=\dfrac{5!}{(5-2)!}=5(4)=20$$

Digit 6 is at the third place

$$P(5,2)=\dfrac{5!}{(5-2)!}=5(4)=20$$ $$20+20=40$$

40 three-digit even numbers can be formed.