PERMUTATION AND COMBINATION

PERMUTATION:Definitoin, Concept , Different Arrangement Of Items, Cyclic Permutation .

A.                Definition, Concept:

Definition: Permutation is defined as the number of arranged of objects. The different orders of arrangement are important. E.g. Find the number of ways of arranging the letters pqr.

Pqr, prq, qrp, qpr, rqp. The number of ways is 6 ways

Similarly, for 4 letters the number of arrangement is 24

In general, the number of different arrangement of n different objects is equal to n! (n factorial)

N! = n x (n-1) x (n-2) x … x 3×2 x 1×0!        (But, 0! = 1)

EVALUATION

1.In how may ways can 8 students be seated in a row?

2.In how many ways can the 1st, 2nd 3rd prizes be won by 6 athletetes in a race?

3.In how many ways can the letters of the word HISTORY be arranged?

 

Example: In how many ways can 6 members of a disciplinary committee be seated round a circular table?

CONDITIONAL PERMUTATION:

Sometimes restrictions are placed on the order of arrangements of objects

Examples:

1.Find the number of ways the letters of the word COMMITTEE can be permuted, if the 2Ts  must always be together.

Solution:

The 2Ts must be together, we can lump them as follows: COMMI (TT) EE = 8!

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