Basic Counting Techniques: Level 1
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Question 1 of 11
1. Question
How many 4-digit numbers have only odd digits?
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Question 2 of 11
2. Question
How many 3-letter words can be formed from the standard 26 -letter alphabet, if the first letter must be a vowel (A, E, I, O, or U)?
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Question 3 of 11
3. Question
How many different three-digit security codes are possible using the digits $1-5$, if the second digit cannot be the same as the first, and third digit cannot be the same as the second?
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Question 4 of 11
4. Question
How many triples
![$\color[rgb]{0.35,0.35,0.35}(a,b,c)$](https://latex.artofproblemsolving.com/e/2/f/e2fafa451a62c3b7f2ed76d692a5c2156a3259ea.png)
of even positive integers satisfy ![$\color[rgb]{0.35,0.35,0.35}a^3 + b^2 + c \leq 50$](https://latex.artofproblemsolving.com/2/4/f/24f3536c2a43c058dc36a202f940b8899702dc39.png)
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Question 5 of 11
5. Question
How many numbers between 100 and 200 (inclusive) are not perfect squares?
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Question 6 of 11
6. Question
How many 3-digit numbers have a first digit which is triple the final digit?
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Question 7 of 11
7. Question
In how many ways can 6 girls and 2 boys sit in a row if the 2 boys insist on sitting next to each other?
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Question 8 of 11
8. Question
How many 4-digit numbers have the second digit even and the fourth digit at least twice the second digit?
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Question 9 of 11
9. Question
How many ways can we put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together? (The math books are all different and so are the English books.)
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Question 10 of 11
10. Question
My school’s Physics Club has 22 members. It needs to select 3 officers: chairman, vice-chairman, and sergeant-at-arms. Each person can hold at most one office. Two of the members, Penelope and Quentin, will only be officers if the other one is also an officer. (In other words, either both Penelope and Quentin are officers, or neither are.) In how many ways can the club choose its officers?
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Question 11 of 11
11. Question
How many positive, even three-digit numbers exist such that the sum of the hundreds digit and the tens digit equals the units digit?
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