問 1
1 点A bakery offers 6 distinct types of cookies and 4 distinct types of muffins. A customer wants to choose a selection consisting of exactly 2 cookies and 1 muffin. How many different selections are possible?
Senior Secondary (HKDSE) · Mathematics
Permutations and combinations ：練習問題
その場で採点される選択問題 5 問と、解説つきの記述問題 5 問。すべて「Permutations and combinations 」からの出題です。
10 問28 点無料・登録不要
問 2
1 点A photographer needs to arrange 7 students, consisting of 4 boys and 3 girls, in a straight line for a group photo. In how many distinct ways can they be arranged if all three girls must always sit together?
問 3
1 点There are 4 distinct boys and 4 distinct girls to be arranged in a straight line. The arrangement must satisfy two conditions: (i) boys and girls must alternate, and (ii) a particular boy, \(B_1\), and a particular girl, \(G_1\), must not sit next to each other.
Find the total number of possible arrangements.
問 4
1 点A bakery offers 5 different types of bread and 4 different types of cake. A customer wants to select 2 distinct types of bread and 1 type of cake. How many different selections are possible?
問 5
1 点A team of 5 people is to be selected from a group consisting of 8 men and 6 women. Find the number of different teams that can be formed if the team must contain at least 4 men.
問 6
3 点How many different ways can 5 distinct books be arranged on a shelf if a particular book must be at the first position?
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 7
4 点A box contains 8 red balls and 6 blue balls. If 4 balls are drawn randomly, how many ways are there to draw at most 1 blue ball?
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 8
6 点In how many ways can 10 different runners be positioned at the starting blocks if runner A and runner B must be in adjacent lanes, and runner C and runner D must not be in adjacent lanes?
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 9
5 点A company team consists of 5 men and 4 women. A committee of 4 people is to be formed from this team.
(a) Find the total number of different committees that can be formed from the team.
(b) Find the number of different committees that can be formed if the committee must consist of exactly 2 men.
(c) Suppose a committee is formed consisting of 2 men and 2 women (as found in (b)). If these 4 committee members are arranged in a straight line for a photograph, find the number of different arrangements such that the 2 men must sit next to each other.
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 10
5 点Eight distinct letters, P, Q, R, S, T, U, V, and W, are to be arranged in a row.
(a) In how many ways can the letters be arranged if P and Q must be together?
(b) In how many ways can the letters be arranged if P and Q must not be together?
まず自分で答えを書いてから、解説と照らし合わせましょう。
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