What are the commonly used permutation and combination formulas?

Commonly used formulas include permutation formulas, combination formulas, repeated permutation formulas, repeated combination formulas, etc. Detailed introduction: 1. Arrangement formula: The number of ways to select m elements from n elements for arrangement: P(n, m) = n! / (n - m)!, The number of full arrangement methods for n elements: P (n, n) = n!; 2. Combination formula: Number of ways to select m elements from n elements for combination: C(n, m) = n! / (m! * (n - m)!) etc.

In permutation and combination, commonly used formulas include:

1. Permutation formula:

   • The number of ways to select m elements from n elements for arrangement: P(n, m) = n! / (n - m)!
   • The number of full arrangement methods for n elements: P( n, n) = n!

2. Combination formula:

   • Number of ways to select m elements from n elements for combination: C (n, m) = n! / (m! * (n - m)!)
   • The number of ways to select m elements from n elements for combination (simplified form): C(n, m ) = C(n, n-m)

3. Repeated arrangement formula:

   • The number of ways to repeatedly select m elements among n elements for arrangement :P'(n, m) = n^m

4. Repeated combination formula:

   • Repeatedly select m elements among n elements. Number of combination methods: C'(n, m) = C(n m - 1, m)

These formulas are very useful when calculating permutation and combination problems and can help determine The total number of options and arrangements of elements. It should be noted that the premise of these formulas is that elements cannot be selected repeatedly. If elements are allowed to be selected repeatedly, repeated arrangement and repeated combination formulas need to be used.

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