How many numbers divisible by 5 and lying between 3000 and 4000 can be formed by using the digits 3, 4, 5, 6, 7, 8 when no digit is repeated in any such number?

Question

Philoid · Accepted Answer

For a number to be divisible by 5, the last digit should either be 5 or 0.

In this case, 5 is only possible.

For a four digit number to be between 3000 to 4000, in this case, should start with 3.

Therefore, the other 2 digits can be arranged by 4 numbers in P(4,2)

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)!

Therefore, a permutation of 4 different objects in 2 places is

P(4,2) =

= = = 12.

Therefore, there are 12 numbers present between 3000 to 4000 formed by using numbers 3,1,5,6,7,8.