數學機率問題(英文)

Q1: How many different numbers can be formed by the product of two or more of the numbers 2

2

3

3

3

5

7

7

7

7?Q2: How many sequences of length 9 formed by using the digits 1

2

3 are there(a) which are increasing (i.e. all 1s before 2s before all 3s) ?(b) without any pair of consecutive digits the same?(c) which contain every digit equally often?(d) which contain the digit 1 exactly five times?Q3: You have invited 10 friends to a party(a) How many ways are there to select a (nonempty) set of guests who have to do the washing-up?(b) How many ways are there to divide your guests into two (nonempty) teams (of possibly different size) ?(c) How many ways are there to divide your guests into two teams of 5 each?(d) How many ways are there to pair your guests off into a collection of5 pairings?Q4: How many ways are there to seat 4 different boys and 4 different girlsaround a circular table? How many ways are there if boys and girlsalternate seats? (At a circular table two seatings which only differ by a rotation are considered equal.)回的好的話會增加贈點謝謝大家的幫忙 ^ ^
Q1: 若包括1以及1與這些數字的乘積

總共有 (2 1)�(3 1)�(1 1)�(4 1) = 120 個組合 但要扣掉1以及1與這四個數的乘積 120－5＝115(個)Q2:(a) which are increasing (i.e. all 1s before 2s before all 3s) ? 假設3個數字都一定要用到 =7 6 5 4 3 2 1 =28 但若假設3個數字不一定要全用到 =10 9 8