Question

If all s's come together, then in how many ways the letters of the word ‘successful be arranged?

Answer 1

Answer

Number of  ways S U C C E S S F U L can be arranged = $\frac{9!}{2!}$ ways

Solution

S U C C E S S F U L  is a 10 letter word. In this word letter 'S' repeat three times, and letter 'C' repeat two times. In this problem one condition is that all S's come together. For solving this problem, we have to consider three 'S' together treated as one digit.

So now we are considering a 9 letter word.

Therefore number of ways  the 9 letters of the word ‘successful be arranged in 9! ways.

But here the letter 'C' is repeating 2 times. We have to divide the result by 2!

Number of  ways S U C C E S S F U L can be arranged = $\frac{9!}{2!}$ ways

Answer 2

successful  is a 10 letter word.  

letter 'S' repeat three times In this word.  . to solve this problem, we have to consider three 'S' together treated as one digit.

So now we will now consider a 9 letter word.

number of ways  the 9 letters of the word ‘successful be arranged in is 9! ways.

similarly the letter "C" is repeating 2 times. We have to divide the result by 2!

so arrangements will be 9!/2!

=9.8.7.6.5.4,3.2/2

=362880/2=181440 arrangement