Multiple choice

The letters of the word 'LEADING' are placed at random in a row. What is the probability that three vowels come together?

  1. 1 35

  2. 1 7

  3. 1 72

  4. 1 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Treat the three vowels as one block. The block and the four consonants can be arranged in 5! ways, while the vowels can be arranged within the block in 3! ways, giving 5! x 3!/7! = 1/7.

AI explanation

The total number of ways to arrange the seven letters in LEADING is 7!, which equals 5040. To find the arrangements where the three vowels (E, A, I) come together, treat them as a single unit. This unit, along with the four consonants, creates five units to arrange in 5! ways. The three vowels can be arranged among themselves within the unit in 3! ways, giving favorable arrangements of 5! times 3!, which equals 120 times 6, or 720. The probability is the ratio of favorable outcomes to total outcomes, so 720 divided by 5040 simplifies to 1 divided by 7.

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