Combinations MATHS - Combinations

Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?

Write the maximum number of points of intersection of 8 straight lines in a plane.

Write the number of diagonals of an n-sided polygon.

Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.

Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.

From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?

How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?

Find the number of diagonals of:

2. A hexagon.
3. A polygon of 16 sides.

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Find the number of:

1. Diagonals.
2. Triangles formed in a decagon.

In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?

In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance of which at least 18 families must have at most 2 children. In how many ways can the choice be made?