Math combinations word problem help?
1. How many 5-card hands that contain exactly 2 aces and 3 kings can be chosen from a 52- card deck? (There are 4 aces and 4 kings in the deck).
2. A wallet contains a nickel, a dime, a penny, and a quarter. How many different sums of money can be made from the change in the wallet?
Please show the work in the form of:
nCr
Best answer will DEFINITELY GET 10 POINTS with work and correct answer.
1. There are
4C2 (= 6) ways to select the 2 aces, and
4C3 (= 4) ways to select the 3 kings.
So, using the general counting principle, there are (4C2)(4C3) (= 24) ways to select 2 aces and 3 kings in the five cards.
2. This one can be done using powers of 2. You can either either select the coin or not. So there are 2*2*2*2 = 16 ways to select the coins (unless you don’t want to include the possiblity that no coins are selected, which means that there are 15 ways).
If you have to use nCr, then there are
4C1 (= 4) ways to select just one coin,
4C2 (= 6) ways to select two coins,
4C3 (= 4) ways to select three coins, and
4C4 (= 1) ways to select four coins.
Since these are mutually exclusive possibilities, then we need to add these. In total, there are 4C1 + 4C2 + 4C3 + 4C4 (= 15) ways.
*********************************
edit: James J, you forgot AH AS and AC AD in your list. That will get you to the 24 combinations total.
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