ARRANGMENT

N terms can be arranged in N! factorial ways, if each position can be occupied by one term.

N terms can be arranged in N^M where. Each position can be occupied by 1 term or 2 terms or …… N terms. M stands for the number of positions to be filled.

COMBINATION

M terms can be selected from P terms in PCm ways.

In certain situations it is required to first choose the terms and then arrange the terms. i.e. PERMUTATION.

Permutation = combination x arrangement.

4. When N objects are distributed among P positions such that each position can get any number of objects (zero, one, two ……N) then the number of ways of arranging the items is N+P-1Cp-1

5. When N objects are distributed among P positions such that each position can get atleast one objet (one, two ……N) then the number of ways of arranging the items is N-1Cp+1

5 crucial points while solving a probability based problem.

1. Calculate the numerator {Nos. of foverable terms} and the denominator {Total number of terms} separately using the concepts of arrangement, permutation and combination.

2. TAKE IT PERSONAL : Always imagine you are arranging / selecting the items. The action of taking the object and placing it in the relevant position is the key.

3. When two or more items are picked it is easier to compute the probability of picking one element at a time than computing the probability of picking many items at a time.

4. When A and B are selected relate the respective probabilities with multiplicataion. When either A or B is selected relate the respective probabilities with addition.

5. When the multiple outcomes are possible the probability of atleast one of them happening is computed by calculating the reverse probability = 1 – probability of event not happening.

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