Question

The letters A, B, C, D, … Z are put into a hat. If four letters...

The letters A, B, C, D, … Z are put into a hat. If four letters are selected one at a time and laid on a table in order, determine the probability that the letters will form the word MATH or LOVE.

Math   Statistics-And-Probability   
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Answer #1

Probability without replacement. Probability = Favorable Outcomes / Total Outcomes

There are 26 alphabets.

Probability Of getting M = 1 / 26

Probability Of getting A = 1 / 25 (since M is already taken out)

Probability Of getting T = 1 / 24

Probability Of getting H = 1 / 23

Therefore probability of getting MATH = (1 / 26) * (1 / 25) * (1 / 24) * (1 / 23) = 1 / 358800

Probability of Getting LOVE in the same way is also = 1 / 358800

Therefore Probability of getting MATH or LOVE = 2 * (1 / 358800) = 1 / 179400

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