NGPF 10.1 Counting Principles

Front

What does 8! (8 factorial) represent?

Back

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320

Front

How do you calculate the number of arrangements of n objects?

Back

The number of arrangements of n objects is given by n! (n factorial).

Front

If Laila can choose from 5 banks and 3 types of accounts, how do you find the total number of choices?

Back

Total choices = Number of banks × Number of account types = 5 × 3 = 15.

Front

How many different 5-digit zip codes can be formed if digits can be repeated?

Back

Each digit has 10 options (0-9), so total zip codes = 10^5 = 100,000.

Front

How many 6-character license plates can be created using 26 letters and 10 digits?

Back

Total characters = 26 letters + 10 digits = 36. Total plates = 36^6 = 2,176,782,336.

Front

What is the formula for permutations of n objects taken r at a time?

Back

P(n, r) = n! / (n - r)!.

Front

What is the difference between permutations and combinations?

Back

Permutations consider order; combinations do not.

Front

How many ways can you arrange 7 students in a row?

Back

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

Front

If you have 3 shirts and 2 pairs of pants, how many outfits can you create?

Back

Total outfits = Number of shirts × Number of pants = 3 × 2 = 6.

Front

What is the factorial of 0?

Back

0! = 1.