11.Permutation and Combination & Factorials

Question 1

What does “n!” represent?

Answer 1

“n!” represents the factorial of a number, which is the product of all positive integers from 1 to n.

Question 2

n!

Answer 2

n * (n - 1)!

Question 3

What is the formula for permutation (nPr)?

Answer 3

The formula for permutation (nPr) is: nPr = n! / (n - r)!

Question 4

What is the formula for combination (nCr)?

Answer 4

The formula for combination (nCr) is: nCr = n! / (r! * (n - r)!)

Question 5

What does “nC0 + nC1 + nC2 + ….. + nCn” represent?

Answer 5

“nC0 + nC1 + nC2 + ….. + nCn” represents the sum of all combinations of choosing 0, 1, 2, …, or all n elements from a set of n elements.

Question 6

nCr

Answer 6

nCn-r

Question 7

nC0 + nC1 + nC2 + ….. + nCn

Answer 7

2^n

Question 8

What is the relationship between permutations and combinations?

Answer 8

Permutations refer to the arrangement of objects in a specific order, while combinations refer to the selection of objects without considering their order.

Question 9

Total number of Handshakes possible among total n people

Answer 9

nC2

Question 10

Total number of Triangles that can be formed by joining sides of
polygon of n sides

Answer 10

nC3

Question 11

What is the formula for calculating the total number of diagonals in a polygon with n sides?

Answer 11

The formula for calculating the total number of diagonals in a polygon with n sides is: (n * (n - 3)) / 2.

Question 12

Total number of circular permutations if clockwise and anti
clockwise are taken as different

Answer 12

(n-1)!