Counting
In how many ways can you choose a team of 6 students from Ms. Math’s class of 10 girls and 5 boys, if the team must consist of 3 girls and 3 boys?
200
9 dogs are having a race. In how many ways can the 1st, 2nd, and 3rd place medals be awarded?
504
How many factors of 9,000 are odd?
12
The parliament of a certain country has 100 members. At least one of them is dishonest. For any pair of members, however, there is at least one honest person. How many of the 100 members are dishonest?
1
Out of a group of 12 hikers, 4 know where to go, and 8 don't. How many ways are there to choose a team of 4 that includes at least 1 hiker who knows where to go?
425
How many ways are there to assign 9 kids to 3 different teams of 3 students each? The teams are named the Red team, the Black team, and the White team and wear colored shirts that match their team name.
1,680
The 6 girls in Ms. Math’s class are going to the movies and will be sitting in a row of 6 seats. In how many different ways can they sit if two of the students, Amy and Bhavya, refuse to sit next to each other?
480
How many 2-digit numbers have digits whose sum is a perfect square?
17
Using each of the 10 digits exactly once, form three positive integers such that their sum S is as small as possible. What is S?
1,674
How many ways are there to distribute 10 identical doggie biscuits among a group of 4 different dogs, if every dog must get at least one biscuit?
84
How many ways are there to rearrange the letters in the word FLAMINGO so that the vowels will be in alphabetical order and so will the consonants? For example, FAGILMON is one such way.
20
A bookbinder must bind 12 identical books using red, green, or blue covers. In how many different ways can this be done? For example one way would be 7 red covers, 2 green covers, and 3 blue covers. Another way would be 12 red covers, and a final example would be 6 green covers and 6 blue covers.
91
What is the sum of all integers between 1000 and 2000 which have all three of the numbers 15, 20, and 25 as factors?
4,500
Evaluate the following (Note the alternating signs both inside and outside the parentheses):
(1 - 2 + 3) - (2 - 3 + 4) + (3 - 4 + 5) - (4 - 5 + 6) + . . . (98 -99 + 100)
-49
There are 13 kids in the Smith family: 8 boys and 5 girls. Two boys, Andy and Ben, just quarreled. In how many ways can Mrs. Smith choose a group of 4 boys and 2 girls if she does not want the group to contain both Andy and Ben?
220