Question

In how many ways can the letters of the word "college" can be arranged such that the 2'L' s come together?​

Answer 1

Answer:

COLLEGE is a 7 letter word.

here E and L will appear for two times so we will get denominator (2!*2!)

so,COLLEGE can be arranged in 7!/(1!*1!*2!*2!*1!)=1260

It is difficult to calculate the case when vowels don't come together so we will be going to calculate the opposite case when vowels do come together.

CLLG(OEE) =4+1 consider OEE as one letteer.

when vowels come together =(5!/2!)*(3!/2!)=180 (3!/2! is the arrangement of vowels total 3 vowels 3! and E repeats two times.)

vowels don't come together =1260-180=1080.