A-level Mathematics/OCR/S1/Probability

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New S1 syllabus does not include lot of these topics

Combinations and Permutations[edit]

Permutation - The total number of ways of arranging r objects from n, where order is important, e.g. choosing a school football team and positions, where anyone can play any position

Combination - The total number of ways of choosing r objects from n, where order is not important, e.g. choosing three cards from a deck, so that you gain a 2, a 3 and a 4 in no particular order

Combinations - Use the button marked nCr on a calculator, or the formula \frac{n!}{(n-r)!r!}

Permutations - Use the button marked nPr on a calculator, or the formula \frac{n!}{(n-r)!}

Probability[edit]

Syllabus Extract:

(a) understand the terms permutation and combination; (b) solve problems about selections, e.g. finding the number of ways in which a team of 3 men and 2 women can be selected from a group of 6 men and 5 women; (c) solve problems about arrangements of objects in a line, including those involving (i) repetition (e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’), (ii) restriction (e.g. the number of ways several people can stand in a line if 2 particular people must — or must not — stand next to each other); (d) evaluate probabilities in simple cases by means of enumeration of elementary events (e.g. for the total score when two fair dice are thrown) or by calculation using permutations and combinations; (e) use addition and multiplication of probabilities, as appropriate, in simple cases; (f) understand informally the meaning of exclusive and independent events, and calculate and use conditional probabilities in simple cases, e.g. situations that can be represented by means of a tree diagram.