Answer:
4pq(p³+q³)
Step-by-step explanation:
Exactly 5 game would be when 4 wins and 1 loss of a particular person
loss has to be one of the first 4 games
A wins: qp⁴ + pqp³ + p²qp² + p³qp
= qp⁴ + qp⁴ + qp⁴ + qp⁴ = 4qp⁴
B wins: pq⁴ + qpq³ + q²pq² + q³pq
= pq⁴ + pq⁴ + pq⁴ + pq⁴ = 4pq⁴
A wins or B wins:
4pq⁴ + 4qp⁴ = 4pq(q³+p³)
Answer: Number of ways 
Step-by-step explanation:
When there is no replacement , we use combination to find the number of ways to choose things.
Number of ways to choose r things out of ( with out replacement) = 
The number of ways to choose 8 things = ![^8C_8=\dfrac{8!}{8!(8-8)!}=\dfrac{1}{0!}=1 [\because 0!=1]](https://tex.z-dn.net/?f=%5E8C_8%3D%5Cdfrac%7B8%21%7D%7B8%21%288-8%29%21%7D%3D%5Cdfrac%7B1%7D%7B0%21%7D%3D1%20%20%5B%5Cbecause%200%21%3D1%5D)
Hence, Number of ways
Answer:
6
Step-by-step explanation:
this should be the correct answer!
1 mile = 6.45 minutes
? miles = 30 minutes
? miles = 30 / 6.45 = 4.65116279 (round up)
4.7 miles = 30 minutes
So roughly 4 and a half miles in 30 minutes
Answer:
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Step-by-step explanation:
C = 2 x r x π = 2 x 9 x π = 18 π cm
