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Combinations

 

Each of the selections that can be made with a given number of objects taken some or all of them at a time is called a Combination.


Result-1 : To find the number of combinations of 'n' dissimilar things taken 'r' at a time :

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Thus, the total number of combinations of 'n' dissimilar things taken 'r' at a time is nCr.

The number of combinations of 'n' dissimilar things taken all at a time = nCn = 1.


Result-2 : To find the number of Combinations of 'n' different things taking some or all at a time :

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Result-3 : The number of selections of some or all out of (p + q + r + ..... ) things out of which p are alike of one kind, q - alike of second kind and so on :

The total number of required ways

= (p + 1) (q + 1) (r + 1) ...... – 1


Result-4 : The number of selections of one or more things from 'p' identical things of one kind, 'q' identical things of a second kind, 'r' identical things of a third kind and 'n' different things

The total number of required ways

= (p + 1) (q + 1) (r + 1) 2n – 1





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