If the letters INTERMEDIATE are arranged, then find the probability that two E's occur together - Maths - Probability

Question

If the letters INTERMEDIATE are arranged, then find the
probability that two E's occur together

Santosh Kumar · Accepted Answer

The total number of arrangements of the letters of the word 'INTERMEDIATE' $= \frac{12!}{(2!) \times (2!) \times (3!)}$

Considering two E' S as one letter, there are 11 letters consisting of two identical T' S, three identical E' S and two identical I' S.

These 11 letters can be arranged in $\frac{11!}{(3!) \times (2!)}$

Probability (two E' S occur together)=

$= \frac{\frac{11!}{(3!) \times (2!)}}{\frac{12!}{(2!) \times (2!) \times (3!)}} = \frac{1}{6}$

If the letters INTERMEDIATE are arranged, then find the probability that two E's occur together .