Question

Four letters are selected at random with replacement from the word MATHCOUNTS. What is the probability that the letters in the order they are selected will form the word MATH?

Answer 1

The no. of letters in the world (MATH) = 4

the no. of favourable outcomes = 10

hence‚ probability of getting the letters (MATH) 2/5

Answer 2

So "MATHCOUNTS" has 10 letters.

And "MATH" has 4 letters.

So the probability of you getting the letters "M" "A" "T" "H" is 4/10 or 2/5.

But it has to be in order...

There are 32 ways you can arrange the 4 letters. There is only 1 way you can write "MATH"

So 1/32 probability of 2/5 is 2/160 or 1/80