Permutations: Distinct Objects

The video tutorial introduces permutations, explaining how to calculate them using factorials. It covers both scenarios where repetition is not allowed and where it is allowed. The tutorial provides examples and solves various permutation problems, including arranging friends for a photo, forming words, and creating security passwords. It also explores practical applications of permutations in real-world scenarios, such as arranging horses in a field and generating car number plates.

How many ways can four friends be arranged in a row for a photograph?

• 120

• 24

• 16

• 4

What is the formula for permutations of n distinct objects taken r at a time?

• n^r

• n!/(n-r)!

• n!/(r!)

• n!/(n-r)!r!

If n = 5, what is the value of 5P3?

• 20

• 120

• 10

• 60

What is the value of n in the equation nP3 = 60?

• 6

• 5

• 4

• 3

When repetition is allowed, how many four-digit codes can be generated from the digits 1, 3, 5, 7, and 9?

• 3125

• 625

• 5000

• 1024

How many ways can three horses graze in a field divided into seven areas, with no two horses in the same area?

• 210

• 343

• 720

• 504

How many three-letter words can be formed from the letters in 'April' without repeating any letters?

• 10

• 20

• 60

• 120

How many security passwords of five characters can be generated from a set of seven distinct characters without repetition?

• 5040

• 2520

• 720

• 1440

How many three-digit numbers greater than 99 can be formed using the digits 2, 4, 6, and 8 with repetition allowed?

• 64

• 81

• 256

• 512

How many car number plates can be created with the format 'AB' followed by four digits, where repetition is allowed but not all digits can be zero?

• 9999

• 9998

• 10001

• 10000