The letters K, O, O, K, and Y can be rearranged to make 5 letter strin

First count the total number of distinct arrangements of the letters without any restrictions.
\(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)

We then have to remove the duplicates coming from the two Ks and two O2
\(2! = 2 \times 1 = 2\)
\(2! = 2 \times 1 = 2\)

\(\frac{5!}{2! \times 2!} = \frac{120}{2 \times 2} = \frac{120}{4} = 30\)

Then we can count the number of arrangements in which the two K's are adjacent by treating the pair "KK" as a single entity.
\(4! = 4 \times 3 \times 2 \times 1 = 24\)

Again we have to remove the duplicates
\(2! = 2 \times 1 = 2\)
\(\frac{4!}{2!} = \frac{24}{2} = 12\)

Subtract the number of arrangements with adjacent K's from the total to get the number with K's not adjacent.
\(30 - 12 = 18\)

Answer 18
Hope this helps!
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