Question

a) How many ways can the letters of the word COMPUTER be arranged in a row?

b) How many ways can the letters of the word COMPUTER be arranged in a row if O and M must remain next to each other as either OM or MO?

c) How many permutations of the letters COMPUTER contain P, U and T (all three of them) not to be together in any order?

Answer 1

a) How many ways can the letters of the word COMPUTER be arranged in a row?

total letter = 8

total positions = 8

no repeatition

first position can be filled by = 8 letters

second position can be filled by = 7 letters {1 has already been used at 1st position}

.....

last position can be filled by = 1 letter

so total combinations = 8*7*....1 = 8! = 40320

b) How many ways can the letters of the word COMPUTER be arranged in a row if O and M must remain next to each other as either OM or MO?

Group O and M as one character and make internal combinations from them

total combinations with 7 letter = 7!

Internal combinations of OM and MO = 2

so total combinations = 2*7! = 10080

c) How many permutations of the letters COMPUTER contain P, U and T (all three of them) not to be together in any order?

answer = Total combinations - combinations where all three of the are put together

combinations where all three of the are put together = internal combinations * combination with 6 words

= 3!*6!

answer = 8! - 3!*6! = 36000