26
– Combinations

Note:
In permutations, order is significant; in combinations, order is *not* significant.

1. Compute the number of 3-combinations of
{ *a, b, c, d*}.

2. List the number of 3-combinations of { *a,
b, c, d*}.

3. How many ways can we select a committee
of 3 from a group of 11 persons?

4. Using a standard 52 card deck,
determine the number of (unordered) five card poker hands containing 4 aces.

5. Using a standard 52 card deck,
determine the number of (unordered) five card poker hands containing all
spades.

Imagine
that the 5 x 7 grid of squares below represents the streets of a part of the
city where you live. You must walk 12
blocks to get from the lower left corner at A to the upper right corner at B.

6. How many 12 block walks are there?

7. How many 12 block walks go through the
corner identified by · ?

8. A shipment consists of 50 microprocessors.
How many ways can we select four microprocessors from the batch?

9. A shipment of 50 microprocessors has
four that are known to be defective. How many ways can we select four
non-defective microprocessors from the batch?

10. A shipment of 50 microprocessors has four
that are known to be defective. How many ways can we select four
microprocessors such that at least one is defective? (more difficult)