3 choose 2 formula 3 choose 2 What if one is asked to determine how many unique combinations of two numbers are possible if one is choosing from a total of three The answer using the ncr formula without repetition above is simply 3 2 3 2 3 2 1 3 2 1 2 1 1 6 2 3 With 3 choose 2 there are just 3 possible
3 choose 2 equals to 3 3C2 3 CHOOSE 2 work with steps provide the detailed information about what is the total number of possible combinations occur nCk while choosing 2 elements at a time from 8 distinct elements without considering the order of elements 3 choose 2 3 choose 2 basically means choosing a number of sampling elements r from the total number of elements in the given set n In this method In other words 3 choose 2 means representing all possible configuration for 3
3 choose 2 formula
3 choose 2 formula
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There are 6 ways to select two items from the set This can be seen in the list of possible combinations shown below 4 Choose 3 This example shows how to calculate the possible ways to select three items from the set of four represented as Finite Math Find the Number of Possibilities 3 choose 2 3C2 C 2 3 Evaluate 3C2 C 2 3 using the formula nCr n n r r C r n n n r r 3 3 2 2 3 3 2 2 Subtract 2 2 from 3 3 3 1 2 3 1 2 Simplify 3 1 2 3 1 2 Tap for more steps 3 3
X 2 x 6 0 x 3 gt 2x 1 x 5 x 5 gt 0 10 1 x 10 4 sqrt 3 x 2 6 11x 6x 2 x 3 0 factor x 2 5x 6 simplify frac 2 3 frac 3 2 frac 1 4 x 2y 2x 5 x y 3 For example you ve got three polynomials p 1 x 1 p 1 x 1 p 1 x 1 p 2 x 3 x 3 p 2 x 3x 3 p 2 x 3 x 3 p 3 x x 2 x 1 p 3 x x 2 x 1 p 3 x x 2 x 1 and you want to express the function q x 2 x 2 x 3 q x 2x 2 x 3 q x 2 x 2 x 3 as a linear combination of those polynomials
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Example in the lock above there are 10 numbers to choose from 0 1 2 3 4 5 6 7 8 9 and we choose 3 of them 10 10 3 times 103 1 000 permutations So the formula is simply nr where n is the number of things to choose from and we choose r of them repetition is allowed and order matters 2 The number of ways to select 3 males out of 7 is 7 choose 3 frac 7 times 6 times 5 3 times 2 times 1 35 Similarly the number of ways to select 2 females out of 5 is 5 choose 2 frac 5 times 4 2 times 1 10 Hence by the rule of product the answer is 35 times 10 350 ways square
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