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3 years ago

Prove that (n-1, r)+(n, r-1)=(n,r)

Mathematics

1 answer:

vlabodo [156]3 years ago

6 0

Answer:

$\binom{n - 1}{r} + \binom{n}{r - 1} = \binom{n}{r} \\( n - 1) + n = n \\ n - 1 = 0 \\ n = 1 \\ r + (r - 1) = r \\ r = 1 \\ \binom{0}{1} + \binom{1}{0} = \binom{1}{1}$

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posledela

Answer:

12 days

Step-by-step explanation:

420/35 to find amount of days to finish book

420/35 = 12

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3 years ago

Tom wants to buy some protein bars and magazines for a trip he has decided to buy three times as many protein bars with magazine

kumpel [21]

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2 years ago

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2 years ago

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the probability that a couple will have two children, so that their first child is a boy and their second child is a girl is 1/2

a_sh-v [17]

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2 years ago

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mixer [17]

Answer: -119, -120, and -121

Step-by-step explanation: This problem states that the sum of three consecutive integers is -354 and it asks us to find the integers. Three consecutive integers can be represented as followed.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since the sum of our three consecutive integers is -354, we can set up an equation to represent this.

X + X + 1 + X + 2 = -354

Now, we can simplify on the left side of the equation.

3x + 3 = -354

-3 -3 ← subtract 3 on both sides of the equation

3x = -357

÷3 ÷3 ← divide both sides by 3

X = -119

X ⇒ first integer = -119

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3 years ago

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Prove that (n-1, r)+(n, r-1)=(n,r)​

Prove that (n-1, r)+(n, r-1)=(n,r)