Question

How many numbers with 6 digits can be formed from the digits 3, 4, 5, 6, 7, 8 if no digit being repeated ? How many of these are
(a) divisible by 5?
(b) not divisible by 5?

Answer 1

Answer:

(a) 120

(b) 600

Step-by-step explanation:

Hi,

We need to form 6 digit numbers using the digits

3,4,5,6,7 and 8 without repetition.

(a)

For a number to be divisible by 5, its last digit should be

5, So, if we fix 5 in units place and then permute the rest

of the 5 digit positions with remaining 5 digits  which

can be done in 5! ways,

Hence,total number of numbers which are divisible by 5

are 5! = 120

(b)

Total number of numbers that can be formed from the

given digits are 6!, of which 5! are divisible by 5 from(a),

so the remaining 6! - 5! = 600 numbers will not be

divisible by 5.

Hope, it helps !