Question

1) How many different ways can you arrange the letters in the words

a) “friends”

b) “initial”

c) “probability”

Show your calculations.

Answer 1

a) “friends”

number of letters = 7

number of repetitions = 0

different ways in which one can the letters = 7! / 0! ( non repetition arrangement of letters )

0! = 1

different ways in which one can the letters = 7!

different ways in which one can the letters = 7*6*5*4*3*2*1

different ways in which one can the letters = 5040

b) “initial”

number of letters = 7

number of repetitions = "i" repeated thrice

different ways in which one can the letters = 7! / 3! ( repetition of one letter thrice in arrangement of letters )

different ways in which one can the letters = 7*6*5*4*3*2*1 / 3*2*1

different ways in which one can the letters = 840

c) “probability”

number of letters = 11

number of repetitions = "i" repeated twice, "b" repeated twice

different ways in which one can the letters = 7! / 2! *2! ( repetition of two letters twice in arrangement of letters )

different ways in which one can the letters = 7*6*5*4*3*2*1 / ( 2*1 * 2*1 )

different ways in which one can the letters = 1260