- #1

CanadianEh

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**What is the probability of...**

**1. Ten cards are dealt from a deck of 156 cards (3 standard 52 card decks) What is the probability of getting at LEAST 3-of-a-kind (up to 10-of-a-kind).**

My Attempt:

**3. P(at least 3-of-a-kind)**

= 1 - P(10 different ranks) - P(9 different ranks)

= 1 - [13C10 * (12C1)^10 + 13C9 * (9C1) * (12C2)^1 * (12C1)^8] / [156C10]

= 1 - [ 286 * 12^10 + 715 * 9 * 66 * 12^8 ] / 1752195368913990

= 1 - 200325892276224 / 1752195368913990

= 1 - 0.1143285137207

= 0.8856714862793

= 1 - P(10 different ranks) - P(9 different ranks)

= 1 - [13C10 * (12C1)^10 + 13C9 * (9C1) * (12C2)^1 * (12C1)^8] / [156C10]

= 1 - [ 286 * 12^10 + 715 * 9 * 66 * 12^8 ] / 1752195368913990

= 1 - 200325892276224 / 1752195368913990

= 1 - 0.1143285137207

= 0.8856714862793

This is a data management question. Please help! Thank you.