(I) Rule of Sums / Inclusion-Exclusion is a strange looking formula. Choose 2 di

Question

(I) Rule of Sums / Inclusion-Exclusion is a strange looking formula.

Choose 2 different numbers from 1 to 20. Let min be the smaller and max be the larger.

You ask Alice to choose a number from 1 to max or from min to 20.
How many different answers can Alice give? Use Inclusion-Exclusion.
Note: You have to use Inclusion-Exclusion. You answer should be 20.

For instance, maybe I choose 15 and 17.
Then Alice is asked to pick from 1 to 17 (17 possible values), or from 15 to 20 (6 possible values).
The number of possible answers is 17 + 6 - _____.

Now ask Alice to choose a number from 1 to min or from max to 20.
How many difference answers can Alice give? Use Inclusion-Exclusion.
Note: If you do Inclusion-Exclusion correctly then your answer will be less than 20.

(II) Now use Rule of Products:

You play matchmaker for a day. There are 20 women and 18 men. You pick one woman and one man to pair up. How many choices do you have for the couple?

You pick a card from a 52 card deck in the following strange way: choose the suit, then choose the face value. How many choices do you have for a card?
Note: You have to use Rule of Products. Hopefully you'll get the "obvious" answer.

Explanation / Answer

(II)

Since 1 woman out of 20 can be choosed in 20 ways and 1 man out of 18 can be choosed in 18 ways so the number fo possible choices you have for the couple is 20*18 = 360

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Since there are 4 suits so we can choose 1 suit out 4 in 4 ways. And in each suit there are 3 cards so number of ways of choosing 1 face card out of 3 is 3. So possibe number of choices for your card is 4*3=12

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