Question

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

Answer 1

Answer: 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 $_nC _r = \frac{n!}{r!*(n-r)!}$ with n = 20 and r = 2 to get the same result.