Combinations MATHS - Combinations

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

1. 60
2. 20
3. 15
4. 125

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.

Evaluate the following:

¹²C₁₀

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if:

1. 4 letters are used at a time.
2. All letters are used at a time.
3. All letters are used but first letter is a vowel?

Evaluate the following:
¹⁴C₃

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?

If ⁿC_p = ⁿC_p Find ¹²C_n.

If ⁿC₁₀ = ⁿC₁₂, Find ²³C_n.

If ¹⁸C_x = ¹⁸C_x+2, Find x.

Find the number of diagonals of:

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

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:

1. No girl?
2. At least one boy and one girl?
3. At least 3 girls?

If ²⁴C_x = ²⁴C_2x+3, Find x.