Shortcut of Combination and Probability

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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