(1) A 5 digit no. is choosen at random. find the probability that the  no. is divisable by 11 and sum  of that no. is 43.

explain me fully.

Let the number be abcde where a,b,c,d and e are integers.

To be divisible by 11   a+c+e-b-d=0 or 11

                                         a+c+e+b+d=43..

For a+c+e-b-d=0 we get b+d=43/2 which is not possible since b,d are integers.

So,a+c+e-b-d=11

b+d=16 and a+c+e=27 now you can use multinomial  .

For a 5 digit number to have sum of digits as 43 ..there are only 2 ways

99988(along with permutations) or 99997(along with permutations)

Out of these there are only 3 cases where the number (upon permutation ) is divisible by 11

98989,97999,99979

Thus the answer is