Question

A student will randomly select 5 cards from a deck of 52 cards. Each card is uniquely identified by a label which is a combination of a letter (one of the following: A, B, C, D) followed by a number (one of the following: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13). The labels on the cards are A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13, C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, D12, D13. What is the probability that the five cards have 4 different number (two cards have the same number and three other cards have three other different numbers)?

Answer 1

The probability that the five cards have 4 different numbers is computed here as:

= Number of ways to select one number from the 13 numbers for which we would have 2 cards * Number of ways to choose 2 cards from 4 cards of that number * Number of ways to select 3 other numbers from remaining 12 numbers * Number of ways to select 1 card each of those 3 numbers / Total ways to select 5 cards from 52 cards

Therefore 0.4226 is the required probability here.