SOLUTION: I need help understanding how to solve these problems....can someone explain them to me... ex... 1) How many 5-card poker hands consisting of 2 aces and 3 kings are possible

Question 88339: I need help understanding how to solve these problems....can someone explain them to me...
ex...
1) How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck?
2) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get exactly 3 apples?
3) How many different three-number "combinations" are possible on a combination lock having 24 numbers on its dial? Assume that no numbers repeat. (combination locks are really permutation locks)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck?
# or ways to pick 2 aces out of 4 = 4C2 = 6
# of ways to pick 3 kings out of 4 is 4C3 = 4
# of ways to pick a 5 card hand out of 52 card = 52C5
P(2 aces and 3 kings) = [6*4]/52C5 = 0.0000092344
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2) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get exactly 3 apples?
# of ways to pick 3 apples = 5C3 = [5*4*3]/[1*2*3] = 10
# of ways to get the orange = 3C1 = 3 ways
# of ways to get exactly 3 apples when pick 4 of the fruit is 10*3=30
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3) How many different three-number "combinations" are possible on a combination lock having 24 numbers on its dial? Assume that no numbers repeat. (combination locks are really permutation locks)
The number of combination s 24C3 = 2024
Since a lock combination depends on the order of the numbers you have to multiply by 3!=6
So, number of combinations is 6*2024 = 12144
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You could get the same answer by thinking the following:
24 ways to pick the 1st number
23 ways to pick the 2nd number
22 ways to pick the 3rd number
Total way = 24*23*22 = 12144
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This is the same as 24P3=12144
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Cheers,
Stan H.

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