a) How many strings are there of length 12 over the alphabet {a, b} with exactly
ID: 3111017 • Letter: A
Question
a) How many strings are there of length 12 over the alphabet {a, b} with exactly five a's? b) How many strings are there of length 12 over the alphabet {a, b, c} with exactly five a's? This question refers to a standard deck of playing cards. A five-card hand is just a subset of 5 cards from a deck of 52 cards. How many different five-card hands are there from a standard deck of 52 playing cards? How many five-card hands have exactly two hearts? How many five-card hands are made entirely of hearts and diamonds? How many five-card hands have four cards of the same rank? e) How many five-card hands do not have any two cards of the same rank.Explanation / Answer
a)
lets put a in 5 places and b in the remaining
number of ways of choosing = 12C5 = 12!/5!*7! = 95040/120
= 792
b)
number of ways of choosing 5 a's= 12C5 = 12!/5!*7! = 95040/120
= 792
b or c in rest 7 places = 2^7
=>
total number of strings = 792 * 2^7 = 101376
4)
a)
number of hands = 52C5 = 2598960
b)
number of ways of picking 2 hearts = 13C2 = 78
number of ways of picking 3 non -hearts = 39C3 = 9139
total number of ways = 9139 * 78 = 712842
c)
number of ways = 26C5 = 65780
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