Permutations
How many 3-digit even numbers can be formed using the digits 1, 2, 3, 4, 5, and 6, if no digit is repeated?
60
From a group of 7 men and 6 women, how many ways can a committee of 5 people be formed if there must be at least 2 women?
1056
In how many ways can the letters of the word "SUCCESS" be arranged such that the two 'S's are never together?
300
How many 4-digit numbers greater than 5,000 can be formed using the digits 0, 1, 2, 3, 4, and 5, if no digit is repeated?
60
A box contains 8 red balls and 6 blue balls. In how many ways can 5 balls be selected if at least 3 must be red?
1036
In how many ways can the letters of the word "ELEPHANT" be arranged such that the vowels always occupy the even positions?
360
A bookshelf has 10 books, including 2 sets of 3-volume books. In how many ways can the books be arranged if the volumes of the same set must stay together?
4320
How many diagonals does a 10-sided polygon have?
35
How many 6-letter words can be formed from the letters of the word "BANANA" if the first and last letters must be 'A'?
12
From a deck of 52 cards, how many 5-card hands contain exactly 3 aces?
4512
In how many ways can 6 boys and 6 girls be seated around a circular table if no two girls can sit together?
86400