Combinatorics

Permutations (k)
$$A_{n}^{k} = \frac{n!}{(n-k)!}$$
(order is relevant)
k - number of elements selected
n - total number of elements
Find   It is known that:
      =   
Calculate 'k'

Permutations
$$P(n) = n!$$
n - total number of elements
Find   It is known that:
      =   
Calculate 'n'

Combinations
$$C_{n}^{k} = \frac{n!}{k!\cdot (n-k)!}$$
(order is irrelevant)
k - number of elements selected
n - total number of elements
Find   It is known that:
      =   
Calculate 'k'

Combinations and permutations
$$A_{k}^{n} = k!\cdot C_{n}^{k}$$
k - number of elements selected
n - total number of elements
Find   It is known that:
      =   
Calculate 'n'

Binomial Theorem
$$T\cdot (k+1) = C_{n}^{k}\cdot a^{(n-k)}\cdot b^{k}$$
Find   It is known that:
      =   
Calculate 'T'

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