Permutations

Example #​1

How many ways can 8 people sit around a circular table?

Given: n = 8​

Solution:​ P = (n-1)!

= (8 - 1)!

​= 7!

​= 7×6×5×4×3×2×1

= 5,040

Example #​2

How many ways can 8 people sit around a circular table if 4 people insist on sitting beside each other?

Given: n = 5​

Solution:​ P = (n-1)!

= (5 - 1)! 4!

​= 4! 4!

​= 4×3×2×1×4×3×2×1

= 576

Example #​3

​

How many ways can the letters of the word

H I G H S C H O O L   be arranged?

Given: n = 10

letter H = 3

letter O = 2​

Solution:​ P=n!/(p!q!r!…)​

= 10!

3! 2!

​= 10×9×8×7×6×5×4×3×2×1

​ 3×2×1×2×1

= 302,400

Example #​3

​

How many ways can the letters of the word

P R E S E N T A T I O N   be arranged?

Given: n = 12

​

letter E = 2

letter N = 2​

letter T = 2​

Solution:​ P=n!/(p!q!r!…)​

= 12!

2! 2! 2!

​= 12×11×10×9×8×7×6×5×4×3×2×1

​ 2×1×2×1×2×1

= 59,875,200