Question

How many terms in the expansion of (x+y+z)^100?

Answer 1

Hey there !!!!!!!!!!

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Number of terms in a multinomial of the form (x+y+z)ⁿ = n+r-1Cr-1

r= number of variables present in multinomial 

Number of terms in (x+y+z)¹⁰⁰ 

n=100 r=3

¹⁰⁰⁺³⁻¹C₃₋₁ = ¹⁰²C₂ = 102!/100!*2! = 101*102/2 = 101*56 = 5656 terms

So (x+y+z)¹⁰⁰ has ¹⁰²C₂=5656 terms in its expansion .

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Hope this helped you...............

Answer 2

Answer:

The right answer is 5151

and the steps of the explanation is in the picture