You are given seven cards numbered 1 through 7. You shuffle the cards and deal them out on a table. What is the probability that the cards will be dealt in order: 1, 2, 3, 4, 5, 6, 7?

Question

kropot72 · Answer

The number of permutations of the seven cards is 7!. The probability of getting any one of these is 1/7!

kropot72 · Answer

@sihelp Do you understand?

accidentalaichan · Answer

I agree with @kropot72. If you are given 7 cards, you have a 1/7 chance of having them pulled in the order given above.

kropot72 · Answer

$$Required\ probability=\frac{1}{7\times6\times5\times4\times3\times2\times1}$$

kropot72 · Answer

There are factorial 7 (7!) permutations of the 7 different cards.
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
The probability of getting any particular one of these 5040 permutations is 1/5040.

anonymous · Answer

oh i just plugged it in it makes more since doing it that way

kropot72 · Answer

@sihelp What did you plug it into?

anonymous · Answer

i used the calculator with scrap paper doing it the same way you just showed me and got the same answer

kropot72 · Answer

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