Math  /  Discrete

QuestionEvaluate the number. C(39,1)C(39,1)

Studdy Solution

STEP 1

1. C(39,1) C(39, 1) represents a combination, which is the number of ways to choose 1 item from 39 items without regard to order.
2. The formula for a combination is given by C(n,r)=n!r!(nr)! C(n, r) = \frac{n!}{r!(n-r)!} .

STEP 2

1. Identify the values of n n and r r .
2. Apply the combination formula.
3. Simplify the expression to find the result.

STEP 3

Identify the values of n n and r r from the combination expression C(39,1) C(39, 1) .
Here, n=39 n = 39 and r=1 r = 1 .

STEP 4

Apply the combination formula C(n,r)=n!r!(nr)! C(n, r) = \frac{n!}{r!(n-r)!} .
Substitute the values of n n and r r :
C(39,1)=39!1!(391)! C(39, 1) = \frac{39!}{1!(39-1)!}

STEP 5

Simplify the expression:
C(39,1)=39!1!38! C(39, 1) = \frac{39!}{1! \cdot 38!}
Since 39!=39×38! 39! = 39 \times 38! , we can cancel 38! 38! in the numerator and denominator:
C(39,1)=39×38!1×38!=391=39 C(39, 1) = \frac{39 \times 38!}{1 \times 38!} = \frac{39}{1} = 39
The value of C(39,1) C(39, 1) is:
39 \boxed{39}

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