Question

how many five digit multiple of 11 are there if the five digits are 3, 4, 5, 6, and 7 in the same order .​ please give me full explanation

Answer 1

Answer:

(A) 12

Step-by-step explanation:

use the following..... successively

1)divisiblity rule for 11

2)permutation

3) basic principle of counting

now.....

part 1 : divisibility rule for 11 says....that the difference of sum of odd positions and even positions of a number is a multiple of 11, then it's divided by 11.

means.....a 5 digit number is of type p q r s t then... (p + r + t) - ( q + s) = 0 or 11 or 22 or 33....

hence....the digits...3, 4, 5, 6, 7 can be arranged like 7 3 6 4 5 which is clearly divisible by 11. bcoz...odd's sum = 7 + 6 + 5 = 18 and even's sum = 3 + 4 = 7 then odd sum - even sum = 18 - 7 = 11

part 2 : the odd's 7, 6, 5 can be arranged in 3! ways themselves and the even's 3, 4 can be in 2! ways within them

part 3 : total number of ways to arrange are 2! × 3! = 2 × 6 = 12 ways ( basic principle of counting)

therefore the number of multiples of 11 are 12