Combinatorics and Logic - Practice

There are seven kinds of fruit sold at a fruitstand in the market. Kate buys here three kinds of fruit, 1 kg of each. How many ways are there for Kate to make her choice?

• 7!

• 210

• 3!

• 24

How many three-digit natural numbers can be assembled from the digits 2, 3, 4, 5, 6, 7, if the digits are not repeated?

• 120

• 720

• 7!

• 3!

How many four-digit numbers are there that are divisible by 3, end with a 5, and in which each of the digits 3; 4; 6 occurs among the digits?

• 24

• 12

• none

• 6

The registration number of a vehicle consists of two letters, three numbers and two letters. How many registration numbers can we form if we use 25 letters and the digits 0-9?

• 390 625 000

• 625 000

• 25²×10³

• 25²×9³

There are 24 boys and 15 girls in a dance circle. How many different pairs can be formed if the dancing couple is always a pair of girl-boy?

• 24! / (24-15)!

• 24!×15!

• 360

• 24! / 15!

In how many ways can 5 students sit around a table, if the orientation of the seating is important?

• 24

• 120

• 12

• 60

8 girls need to be arranged around a table. Two among them always sit together. In how many ways can they be arranged?

• 8!

• 7! × 2

• 6!

• 6! × 2

Amy, Ben, Claudia and Dan are sitting down randomly on a bench, next to one another. In how many different ways can it happen that neither the two boys (Ben and Dan), nor the two girls (Amy and Claudia) are sitting next to each other?

• 24

• 8

• 12

• 6

The number of permutations of the letters in the word MICHIGAN is _____.

• 40320

• 5040

• 7!

• 20160

8 persons attended an interview at a company where each person can be either selected or rejected. Find the number of ways of announcing the result.

• 8!

• 2⁸

• 8²

• 7!