# 90+ Permutations Combination And Probability Question PDF

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## Permutation and Combination

• Permutation: It is the different arrangements of a given number of elements taken one by one, or some, or all at a time. For example, if we have two elements A and B, then there are two possible arrangements, AB and BA.
• Number of permutations when ‘r’ elements are arranged out of a total of ‘n’ elements is nPr = n! / (n – r)!. For example, let n = 4 (A, B, C and D) and r = 2 (All permutations of size 2). The answer is 4!/(4-2)! = 12. The twelve permutations are AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB and DC.
• Combination: It is the different selections of a given number of elements taken one by one, or some, or all at a time. For example, if we have two elements A and B, then there is only one way select two items, we select both of them.
• Number of combinations when ‘r’ elements are selected out of a total of ‘n’ elements is n C r = n! / [ (r !) x (n – r)! ]. For example, let n = 4 (A, B, C and D) and r = 2 (All combinations of size 2). The answer is 4!/((4-2)!*2!) = 6. The six combinations are AB, AC, AD, BC, BD, CD.
• n C r = n C (n – r)

NOTE: In the same example, we have different cases for permutation and combination. For permutation, AB and BA are two different things but for selection, AB and BA are the same.

## Probability

Introduction

Probability is the likelihood or chance of an event occurring.

 Probability = the number of ways of achieving success the total number of possible outcomes

For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting ahead and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½.

• The probability of something which is certain to happen is 1.
• The probability of something which is impossible to happen is 0.
• The probability of something not happening is 1 minus the probability that it will happen.

This video is a guide to probability. Expressing probability as fractions and percentages based on the ratio of the number ways an outcome can happen and the total number of outcomes is explained. Experimental probability and the importance of basing this on a large trial is also covered.

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