how many arrangements can be made from the letters of the wo

how many arrangements can be made from the letters of the word French if
a. all the letters are used
b. three of the letters are used
c. four of the letters are used

Solution

a) FRENCH

All letter used = 6 letters so 6! arrangements can be made

6! = 720

b) Three letters used.

Choose three of 6 letters in 6C3 ways

Arrange those 3 in 3! ways

So, total = 6C3 * 3! = 20 * 6 = 120

c) four of the letters are used:

Choose four of 6 letters in 6C4 ways

Arrange those 4 in 4! ways

So, total = 6C4 * 4! = 15 * 24 = 360