How many permutations of the letters ABCDEFGH contain the le

How many permutations of the letters ABCDEFGH contain the letters ABCFG together in any order? How many distinct permutations can be made from the characters in the word GOOGLE?

Solution

there are 4!*4! ways to permutations of the letters ABCDEFGH contain the letters ABCFG together in any order.

consider ABCFG as 1 letter. hence total no of permutation are 4! =4*3*2*1=24.no wfor permutation of ABCFG is also 4! hence ans is 4!*4!=576

for the google permutation since o is repeted 2 times and also g.ans is 6!/(2!*2!)=180