steven has 10 different shirts 6 different hats 4 different scarves. Steven thinks that if he picks just two of the three items of clothing there will be more than 240 combinations. is the correct

No, he is not correct

The number of combinations is 190

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Work Shown:

We have 10 shirts, 6 hats, and 4 scarves. This is 10+6+4 = 20 items total.

If we randomly pick out an item, then we have 20 to choose from. After selecting that first item, we have 20-1 = 19 items left to choose from.

So there are 20*19 = 380 different permutations. Order matters with permutations.

Since we aren't worried about order, this means that we've double counted so we have to divide by 2 to fix it.

So there are 380/2 = 190 combinations.

You can use the nCr combination formula with n = 20 and r = 2 to get the same result.

There are four aces, 12 face cards and 4 7s in a standard 52 card deck. The probability of getting an ace on the first draw is 4/52 or 1/13. For the second draw there are now 51 cards in the deck (assuming the draws are without replacement), so the probability of getting a face card is 12/51. Given an ace and a face card on the first two draws, the probability of a 7 on the third draw is 4/50 or 2/25. The probability of getting all three is 1/13*12/51*2/25.
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