- #1
lee534
- 7
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Hi all I need some assistance
1. Homework Statement with the attempt
How many 5-digit briefcase combinations contain
1. Two pairs of distinct digits and 1 other distinct digit. (e.g 12215)
I wasn't sure on which approach was correct.
10 * 9 * 8 (because there are three distinct digits)
or
10C2 * 5C2* 3C2 * 8 (because you have to take into account how the doubles can be orientated)
2. A pair and three other distinct digits. (e.g 27421)
same issue as above
10*9*8*7
or
(5C2*10) * 9 * 8 * 7
lastly
I have found this question before but I couldn't get an explanation:
How many ways are there to pick a collection of 12 coins from piles of pennies, nickels, dimes, quarters, and half-dollars? Base on the following condition:
1. there are only 10 coins in each pile.
16C4 - 5^2 because it's the total minus how many ways I can get from the 11th coin and the 12th coin. = 1795
2. There are only 10 coins in each pile and the pick must have at least one penny and two nickels?
1795 - 13C4(?)
my logic is that it's because 12-3+4 C 4 but I'm not sure if I have to set it to 12 or 10.
Thank you!
1. Homework Statement with the attempt
How many 5-digit briefcase combinations contain
1. Two pairs of distinct digits and 1 other distinct digit. (e.g 12215)
I wasn't sure on which approach was correct.
10 * 9 * 8 (because there are three distinct digits)
or
10C2 * 5C2* 3C2 * 8 (because you have to take into account how the doubles can be orientated)
2. A pair and three other distinct digits. (e.g 27421)
same issue as above
10*9*8*7
or
(5C2*10) * 9 * 8 * 7
lastly
I have found this question before but I couldn't get an explanation:
How many ways are there to pick a collection of 12 coins from piles of pennies, nickels, dimes, quarters, and half-dollars? Base on the following condition:
1. there are only 10 coins in each pile.
16C4 - 5^2 because it's the total minus how many ways I can get from the 11th coin and the 12th coin. = 1795
2. There are only 10 coins in each pile and the pick must have at least one penny and two nickels?
1795 - 13C4(?)
my logic is that it's because 12-3+4 C 4 but I'm not sure if I have to set it to 12 or 10.
Thank you!