probability (permulation and combination)

heng87

1)Four people A,B,C and D apply for two vacancies as senior engineer and junior engineer.Find the total number of ways of filling up the two vacancies.

为什么是4P2不是4C2？我不知道什么时候用permulation 和 combination。可以解释和给一些example.

2)Four letters are selected from the word 'SENDING'.Find the number of words with four letters that does not contain N?

SOLUTION
Without letter N,4 letters can be chosen from{S,E,D,I,G}.Thus, the number of selections of 4 letters from the 5 letters=5C4=5.Now,each selection of 4 letters can arranged in 4! ways.thus the number of arrangements=24x5=120.
为什么是5C4不是5P4?

bryanliau91

回复 1# heng87

1)"senior engineer and junior engineer"
有注明的.

就是说这题是有arrangement,所以用Permutation.


假如问题问:"two engineers",那就用Combination

2)Four letters are selected from the word 'SENDING'.Find the number of words with four letters that does not contain N?



就是说,要从{S,E,D,I,G}抽四个letters出来.
题目没有说会replacement the letter which drawn back into the box.
就是说抽了就没有可能再抽回同样的字母.

所以用factorial.

5 x 4 x 3 x 2 = 120

heng87

回复 2# bryanliau91


    谢谢你的帮助

bryanliau91

回复 3# heng87
不客气~最近有读到而已~

heng87

回复 4# bryanliau91
[求助] mathematical expectation

a student guesses at random each and every one of the 50 objective questions in a PMR examination.If each question has 4 possible answers,what is the variance of X,where X is the number of questions answered correctly? 答案是9.375.我不是很明白题目的意识。请解释题目的意识和如何算到答案 two badminton players,Alan and Brown,are to play in a match for a wager.The first person to win sets in a row,or two out of three sets wins the match.If Alan wins the match,Brown pays him b ringgits per played,whereas if Brown wins the match,Alan pays Brown a ringgit per set played.The probability of Alan winning the first set is 2/3.However,Alan is a veteran player who tires easily to the extent that subsequently his probability of winning any set is one half that of winning the previous set.Find the ratio a:b which makes the wager "fair" to both players. 答案是a:b=13:33 .我不是很明白题目的意识。请解释题目的意识和如何找到答案