- #1
modulus
- 127
- 3
I solved a problem, by two different, and (apparently) viable solutions. But, each solution led me to a different answer:
The question asks me to find out the number of possible ways in which I can choose 5 cards from a standard pack of 52 cards, so that I choose at least a single card from each suite.
FIRST METHOD:
One card from each suite of 13 means a total of [13C1 * 13C1 * 13C1 * 13C1].
After that, I'll have 52-4=48 cards left from which I need to choose only one. That means 48C1.
The final result:
13C1 * 13C1 * 13C1 * 13C1 * 48
SECOND METHOD:
I'll be choosing one card from three suites, but exactly two cards from the fourth suite. So that means:
13C1 * 13C1 * 13C1 * 13C2
= 13C1 * 13C1 * 13C1 * 13C2 * (12/2)
And since I do this with each of the four suites (choose two from it only, while taking one from each of the others), I shall multiply this by 4, giving me:
13C1 * 13C1 * 13C1 * 13C2 * 24
And this is half of the answer arrived at by the first method...
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what went wrong?
The question asks me to find out the number of possible ways in which I can choose 5 cards from a standard pack of 52 cards, so that I choose at least a single card from each suite.
FIRST METHOD:
One card from each suite of 13 means a total of [13C1 * 13C1 * 13C1 * 13C1].
After that, I'll have 52-4=48 cards left from which I need to choose only one. That means 48C1.
The final result:
13C1 * 13C1 * 13C1 * 13C1 * 48
SECOND METHOD:
I'll be choosing one card from three suites, but exactly two cards from the fourth suite. So that means:
13C1 * 13C1 * 13C1 * 13C2
= 13C1 * 13C1 * 13C1 * 13C2 * (12/2)
And since I do this with each of the four suites (choose two from it only, while taking one from each of the others), I shall multiply this by 4, giving me:
13C1 * 13C1 * 13C1 * 13C2 * 24
And this is half of the answer arrived at by the first method...
.
.
.
.
.
.
.
what went wrong?