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1.Description
In mathematics, the binomial coefficient is defined as the coefficient of (1 + x)ⁿ when expanded, where n is a natural number, and k is an integer. Its value equals the combination number, n!/((n–k)! k!)
2.Understanding Functions
Combinationnchoosek
Permutationsperms
3.Programming Practice for Solving Permutation and Combination Problems
(1) Select any 3 numbers from the four numbers 1, 2, 3, 4 and find all combinations and the number of combinations
(2) Select any 2 letters from the three letters a, b, c and find all combinations and the number of combinations
(3) Find all permutations and the number of permutations of the three numbers 1, 2, 3
(4) Find all permutations and the number of permutations of the three letters a, b, c
The Matlab program code is as follows:
ans1=nchoosek(1:4,3) %Combination
ans1 =
1 2 3
1 2 4
1 3 4
2 3 4
ans2=nchoosek(4,3) %Number of Combinations
ans2 =
4
ans3=nchoosek(‘abc’,2)
ans3 =
3×2 char array
‘ab’
‘ac’
‘bc’
ans4=nchoosek(3,2)
ans4 =
3
ans5=perms(1:3) %Permutations
ans5 =
3 2 1
3 1 2
2 3 1
2 1 3
1 3 2
1 2 3
ans6=perms(‘abc’)
ans6 =
6×3 char array
‘cba’
‘cab’
‘bca’
‘bac’
‘acb’
‘abc’
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