Combinatorics

There are seven kinds of fruit sold at a fruit stand in the market. Kate buys 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

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

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!

Tags

CCSS.HSF-LE.A.1B

A question paper consists of two sections each containing 6 multiple choice questions. Each question of the first section has 3 choices and each question of the second section has 2 choices. In how many different ways can a student answer the question paper?

• 6³ × 6²

• 6! × 2!

• 3⁶ × 2⁶

• 3! × 2! × 6

Find the number of ways of selecting 2 vowels and 2 consonants from the letters of the set {I, N, T, E, R, V, A, L}.

• 30

• 10

• 13

• 70

In a group of 20 members, 12 are boys and 8 are girls. Find the number of ways of forming a 15 member committee which should include exactly 9 boys.

• 15504

• 167960

• 220

• 6160