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Load Combinations Book EC3 - BCSA
Permutations and Combinations
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Permutations of n different items o
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What we mean by a permutation, and how to work them out for n different items. You You are also given 3 questions to answer. (1) In how many different ways can you arrange 6 people in a line? (2) How many different numbers can be formed from the digits 1, 2, 3, , !, 6 and " if each digit is used only once? (3) How many different car registration registration plates can be mad e consisting of the letters #, $ and %, the numbers 1, 2, 3 and where the 3 letters appear before the four numbers and each number and letter can appear once in each registration registration plate?
Permutations of r items from n different items
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Permutations of repeated letters in a word
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How to calculate how many arrangements arrange ments of r items taken from n items. introduce the formula nPr and show you it on a calculator. You You are also given this question " people get into a train but only seats are a&ailable' How many different ways are of there of seating people?
How to calculate how many arrangements arrange ments or permutations there are of letters in a word where a letter is repeated. !he following e"amples are given. (1) In how many ways can the letters in the word EYE be be arranged? (2) In how many ways can the letters in the word STATIST STATISTIC IC be arranged?
Permutations with restrictions# letters $ items together
How to calculate how many arrangements arrange ments or permutations when letters or items are to stay together. toge ther. !he following e"amples are given with worked solutions. 1) In how many ways can the letters in the word H* be arranged where the +s are together? 2) In how many ways can 3 women and men sit in a line if the women always sit together?
3) How many ways can the letters in the word #-# #-# be arranged if the and - are together?
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Permutations with restrictions # items at the ends
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Permutations with restrictions # items must not be together
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How to calculate how many arrangements arrange ments or permutations when letters or items are restricted to the ends of a line. !he following e"amples are given with worked solutions. 1) In how many ways can 2 men and 3 women sit in a line if the men must sit on the ends? 2) In how many ways can 3 blue boo.s and red boo.s be arranged on a shelf if a red boo. must be on each of the ends assuming that each boo. loo.s different e/cept for colour'
How to calculate how many arrangements arrange ments or permutations when letters or items are restricted to being seperated. !he following e"amples are given with worked solutions. (1) In how many ways can ! men and 3 women be arranged in a row if no two women are standing ne/t to one another? (2) In how many ways can the letters in the word 0%%00 be arranged if no two 0+s are ne/t to one another?
%ombinations of n different items o
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What a combination is, how to calculate it using the n%r function and answer the following question. How many different combinations (selections) (selections) of 3 letters can be made from the the ! letters #$% ?
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%ombining combinations
&"tend the work to cover combining c ombining combinations. !he following e"amples are used.
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1) How many ways can a committee be formed consisting of 3 men and 2 women selected from " men and 1 women? 2) 4i&e letters are to be selected from the letters in the word #5#7# #5#7#8' 8' How many different combinations are there?
Permutations and %ombinations in probability How to use permutations use permutations and combinations to work out probabilities. •
' committee of ( people is to be selected from a group of ( men and ) women. What is the probability that the committee contains * men and 3 women+
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&ach of ( cards has one of the letters ', , %, - and & written on them. !he cards are shuffled. What is the probability that the letters ' and are together+