In how many ways can the letters of the word PSYCHOLOGY be rearranged so that the
two "O's do not appear together?
Answers
Given : word PSYCHOLOGY
letters of the word PSYCHOLOGY be rearranged so that the two "O's do not appear together
To Find : Number of ways
Solution:
PSYCHOLOGY
Total Letters = 10
Y , O = 2 times each
Total Possible arrangement = 10!/2! .2!
Assume that two O comes together
Then taking two O as 1 letter
Then total 9 letters and Y is repeated twice
Hence arrangements = 9! / 2!
Hence Number of ways two "O's do not appear together
= 10!/2! .2! - 9!/2!
= 5* 9!/2! - 9!/2!
= 4 * 9!/2!
= 2 * 9 !
= 7,25,760
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