Misc 8 - Determine number of 5 card combinations out of 52 - Combination

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise
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Misc 8 Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. There are total 4 King Cards out of 52 We have to select one King from 4 King Total number of ways = 4C1 × 48C4 = 4!/1!(4 − 1)! × 48!/4!(48 − 4)! = 4!/1!3! × 48!/4!44! = 48!/(3! × 44!) = (48 × 47 × 46 × 45 × 44!)/((3 × 2 × 1) × 44!) = 778320

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.