Multiple choice

A bag contains $20$ cards $10$ of these cards have letter $'E'$ $5$ have letter $'I'$ and other $5$ have letter $'A'$ printed on them, if five cards are drawn one by one and are kept in same order aside then probability of making the words $AIEEE$ is

  1. $5/36$
  2. $25/2584$
  3. $36/2584$
  4. $26/37$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total cards = 20. Cards: 10 E, 5 I, 5 A. We need A, I, E, E, E in that order. P(A) = 5/20. P(I) = 5/19. P(E) = 10/18. P(E) = 9/17. P(E) = 8/16. Multiply: (5/20)(5/19)(10/18)(9/17)(8/16) = 25/2584.

AI explanation

The word AIEEE requires drawing 1 A, 1 I, and 3 E's in that specific order. The probability of drawing an A first is 5/20, then an I is 5/19, and then three E's are 10/18, 9/17, and 8/16. Multiplying these independent probabilities gives (5/20) times (5/19) times (10/18) times (9/17) times (8/16), which simplifies to (1/4) times (5/19) times (5/9) times (9/17) times (1/2). This equals 25 divided by (4 times 19 times 17 times 2), resulting in 25/2584.

Keep practicing — related questions