Question

Consider the word "TUMBARUMBA"

a)How many words can be made by arranging all 10 letters?

b)How many of these words included TU as a subword?

Answer 1

a.

no. of words

= (no. of letters)! / (product of k!)

{where k are no. of times each unique letter is there in "TUMBARUMBA"}

= 10! / [1! * 2! * 2! * 2! * 2! * 1! ]

= 226800 words

b.

for including TU let us cinsider it as a separate unique letter

{now only 9 letter, and u will be considered as only appearing 1 time because the other U is included in TU which is a separate letter now}

no. of words

= (no. of letters)! / (product of k!)

{where k are no. of times each unique letter is there in "TUMBARUMBA"}

= 9! / [1! * 2! * 2! * 2! * 1! * 1! ]

= 45360 words

(please UPVOTE)