Answer :
36 number of ways to set out the letters without the i's together.
Order of the letters matters, so, this is a permutation problem.
Now we will determine in how many ways we can arrange these letters.
There are 2 repeating i's, so, we can arrange the letters:
5!/2! = 120/2
= 60 ways.
We also have the following equation:
60 = (number of ways to arrange the letters with the i's together) + (number of ways without the i's together).
To find the no. of ways to set out the letters with the i's together.
We have: [i-i] [d] [g] [t]
We see that with the i's together, we have:
4! = 24 ways to arrange the letters.
Thus, the number of ways to set out the letters without the i's together is:
60 – 24 = 36.
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