Question

If repetitions are not permitted
(i) How many $3$ digit numbers can be formed from the six digits $2,3,5,6,7,9$?
(ii) How many of these are less than $400$?
(iii) How many are even?
(iv) How may are odd?
(v) How many are multiples of $5$?

Answer 1

solution:

1. 3 digits formed from 2, 3, 5, 6, 7, 9

Permutation formula $=\frac{n!}{(n-r)!}$

$=\frac{6!}{(6-3)!}$

${}_3^{6}P=66\times 5\times 4$

$=120$

2. Numbers less than 400 can start with digits 2 and 3 only.

$2\times 6\times 6=72$

3. Even numbers are 2 and 6 from the given 6 digits.

$2\times 6\times 6=72$

4. Odd numbers are 3, 5, and 7 from the given 6 digits.

$6\times 6\times 3=108$

5. 5 is the only digit from 6 digits have multiples of 5.

$6\times 6\times 1=36$.