11.From 4 officers and 8 jawans, a committee of 6 is to be chosen to include exactly one officer. The number of such committees is

12.How many numbers greater than 1000, but not greater than 4000 can be formed with digits 0, 1, 2, 3, 4 repetitions of digits being allowed?

13.A five-digit number divisible by 3 is to be formed using the numerals 0, 1,2,3,4 and 5 without repetition. The total number of ways this can be done is

14.Mr. A has x children by his first wife and Ms. B has x+1 children by her first husband. They marry and have children of their own. The whole family has 10 children. Assuming that two children of the same parents do not fight, the maximum number of fights that can take place among the children is

15.Five distinct letters are to be transmitted through a communication channel. A total number of 15 blanks is to be inserted between the two letters with at least three between every two. The number of ways in which this can be done