A convex polygon has 44 diagonals. Find the number of its sides

18 mice were placed in two experimental groups and one control group, with all groups equally large. In how many ways can the mice be placed into three groups?

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if (a) they can be of any colour (b) two must be white and two red and (c) they must all be of the same colour.

In how many ways can a football team of 11 players be selected from 16 players?
How many of them will
(i) include 2 particular players?
(ii) exclude 2 particular players?

A sports team of 11 students is to be constituted, choosing at least 5 from Class XI and atleast 5 from Class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted?

A group consists of 4 girls and 7 boys. In how many ways can a team of 5
members be selected if the team has
(i) no girls
(ii) at least one boy and one girl
(iii) at least three girls.

The number of possible outcomes when a coin is tossed 6 times is
(A) 36
(B) 64
(C) 12
(D) 32

The number of different four digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is
(A) 120
(B) 96
(C) 24
(D) 100

The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is
(A) 432
(B) 108
(C) 36
(D) 18

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
(A) 60
(B) 120
(C) 7200
(D) 720

A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4  and 5 without repetitions. The total number of ways this can be done is
(A) 216
(B) 600
(C) 240
(D) 3125