H Algebra 2/Trig · Unit 8
Multiply the number of choices for each place. Watch for repeats and for a first digit that cannot be 0.
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Multiply the choices
If the choices are made one after another, multiply how many options each place has.
Repeats and a first digit
If repeats are allowed, a place keeps its full list of options.
If the first digit cannot be 0, that place has 9 options, not 10.
Repeats are allowed
Repeats are allowed, so every place has the same number of choices.
10 × 10 × 10 × 10
10,000
Answer: 10,000
Repeats are allowed, so every place has the same number of choices.
10 × 10 × 10
1,000
Answer: 1,000
Repeats are allowed, so every place has the same number of choices.
10 × 10 × 10 × 10 × 10
100,000
Answer: 100,000
Repeats are allowed, so every place has the same number of choices.
26 × 26
676
Answer: 676
Repeats are allowed, so every place has the same number of choices.
8 × 8 × 8
512
Answer: 512
Repeats are allowed, so every place has the same number of choices.
10 × 10 × 10 × 10 × 10 × 10
1,000,000
Answer: 1,000,000
The first digit cannot be 0
The first digit has 9 choices, 1 through 9.
Each later digit has 10 choices, 0 through 9, and repeats are allowed.
9 × 10 × 10 × 10 × 10
90,000
Answer: 90,000
The first digit has 9 choices, 1 through 9.
Each later digit has 10 choices, 0 through 9, and repeats are allowed.
9 × 10 × 10
900
Answer: 900
The first digit has 9 choices, 1 through 9.
Each later digit has 10 choices, 0 through 9, and repeats are allowed.
9 × 10 × 10 × 10
9,000
Answer: 9,000
The first digit has 9 choices, 1 through 9.
Each later digit has 10 choices, 0 through 9, and repeats are allowed.
9 × 10 × 10 × 10 × 10 × 10
900,000
Answer: 900,000
The first digit has 9 choices, 1 through 9.
Each later digit has 10 choices, 0 through 9, and repeats are allowed.
9 × 10
90
Answer: 90
The first digit has 9 choices, 1 through 9.
Each later digit has 10 choices, 0 through 9, and repeats are allowed.
9 × 10 × 10 × 10 × 10 × 10 × 10 × 10
90,000,000
Answer: 90,000,000
No repeats, and the first digit cannot be 0
The first digit has 9 choices, 1 through 9.
No digit repeats, and 0 is available after the first digit.
9 × 9 × 8 × 7
4,536
Answer: 4,536
The first digit has 9 choices, 1 through 9.
No digit repeats, and 0 is available after the first digit.
9 × 9 × 8
648
Answer: 648
The first digit has 9 choices, 1 through 9.
No digit repeats, and 0 is available after the first digit.
9 × 9 × 8 × 7 × 6
27,216
Answer: 27,216
The first digit has 9 choices, 1 through 9.
No digit repeats, and 0 is available after the first digit.
9 × 9 × 8 × 7 × 6 × 5
136,080
Answer: 136,080
The letters do not repeat.
26 × 25
Each digit has 10 choices, and digits may repeat.
10 × 10 × 10
26 × 25 × 10 × 10 × 10
650,000
Answer: 650,000
Nothing repeats inside the letters, and nothing repeats inside the digits.
26 × 25 × 24 × 10 × 9
1,404,000
Answer: 1,404,000
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