Permutation and Combination Formulas Factorial
n ! = n(n1)(n2) …… 1 Eg. – 5! = 5(51)(52)(53)(54) = 5(4)(3)(2)(1)
Number of ways in which Permutations out of n things r things can be SELECTED & ARRANGED (denoted by ^{n}P_{r}).
^{n}P_{r} = number of permutations (arrangements) of n things taken r at a time.
Eg.
Formulas for Combinations
The number of ways in which r things at a time can be SELECTED from from n things is Combinations (represented by ^{n}C_{r}).. ^{n}C_{r} = Number of combinations (selections) of n things taken r at a time.
Eg.
Property 1
Number of permutations (or arrangements) of n different things taken all at a time = n!
Property 2
For Objects in which P1 are alike and are of one type, P2 are alike or other different type and P3 are alike or another different type and the rest must be all different, Number of permutations =
Property 3
When repetition is allowed number of permutations of n different things taken r at a time = n × n× n ×… (r times) = n^{r}
Property 4
Here, we are counting the number of ways in which k balls can be distributed into n boxes under various conditions. The conditions which are generally asked are
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