On how many ways can the letters of the word "COMPUTER" be arranged?
1. M must always occur at the third place
2. Vowels occupy the even positions.
Soln: For 1.
7*6*1*5*4*3*2*1=5,040
For 2.) I think It should be 4 * 720
there are 4 even positions to be filled by three even numbers.
in 5*3*4*2*3*1*2*1 It is assumed that Last even place is NOT filled by a vowel. There can be total 4 ways to do that.
Hence 4 * 720
My question is regarding the second part of the question
where we are calculating the ways in which vowels can be arranged
shouldnt it be
n!/(n-r)! RESULTING IN 24*720 as the order does matter
rather than n!/(n-r)!*r! which results in 4*720 order doesnt matter
the order should matter as e.g abc is not the same as cba when finding ways to arrange words
can someone please help
thanks
1. M must always occur at the third place
2. Vowels occupy the even positions.
Soln: For 1.
7*6*1*5*4*3*2*1=5,040
For 2.) I think It should be 4 * 720
there are 4 even positions to be filled by three even numbers.
in 5*3*4*2*3*1*2*1 It is assumed that Last even place is NOT filled by a vowel. There can be total 4 ways to do that.
Hence 4 * 720
My question is regarding the second part of the question
where we are calculating the ways in which vowels can be arranged
shouldnt it be
n!/(n-r)! RESULTING IN 24*720 as the order does matter
rather than n!/(n-r)!*r! which results in 4*720 order doesnt matter
the order should matter as e.g abc is not the same as cba when finding ways to arrange words
can someone please help
thanks
