Shortcut of Combination and Probability

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Shortcut 99:    nCr=n!/[r!(n-r)!] Question: In how many ways 2 shirts and 3 pants can be selected from 5 shirts and 7 pants? Answer: Selecting 2 shirts out of 5 = 5C2 = 5!/[2!(5 – 2)!] = 10 Selecting 3 shirts out of 7 = 7C3 = 7!/[3!(7 – 3)!] = 35 Since the two events are dependent, Total ways of selecting = 10 x 35 = 350 Probability Shortcut 100:                   Probablity=Expected number of result / Total number of result Question: What is the probability of selecting 2 spades from a pack of 52 cards? Answer: Total number of ways of selecting 2 cards from 52 = 52C2 = 1275 Total ways of selecting 2 spades from 13 spades = 13C2 = 78 Probability = 78/1275]]>

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