Find the number of ways to arrange the letters of the word ' GOODFRIDAY ' if letters ' DAY ' are alw

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15 Apr 2022 Permutation & Combination

Find the number of ways to arrange the letters of the word ' GOODFRIDAY ' if letters ' DAY ' are always together.

OPtion

1) 1814400
2) 151200
3) 907200
4) 241920
5) 120960
6) 15120
7) 60480
8) 30240
9) 45360
10) None of these

Solution

The word GOODFRIDAY has 10 different letters
When the letters DAY are kept together they can be supposed to form one letter.
Then we have to arrange letters GOODFRI (DAY)
Now 8 letters (7+1) can be arranged in 8!/2! (O being repeated twice)
The letters DAY can be arranged among themselves in 3! ways.
.'. Required number of ways = (8!/2!)*3! = 120960

Correct Option: 5 Best Solution (1)

Mayank Kandoi   2 years AGO

Treat the letters DAY as one unit.
Total combinations = (8!/2!) * 3! = 120960

Option 5

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