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kolezko [41]
3 years ago
11

In how many ways can 6 competitors finish a race assuming there are no ties?In how many ways can we sit n people on r < n cha

irs? In how many wayscan the gold, silver and bronze medals be awarded in a race of 8 people? Howmany 5-digit zip-codes are possible? How many different 3-person committeeswe can make with 10 people?
Mathematics
1 answer:
VLD [36.1K]3 years ago
6 0

Answer:  a) 720, b) ^nC_r=\dfrac{n!}{(n-r)!r!} c) 336, d) 30240 e) 120.

Step-by-step explanation:

Since we have given that

a) Number of competitors  = 6

We need to find the number of ways that 6 competitors can finish a race and there are no ties.

So, Number of ways would be

6!=720

b) number of people = n

Number of chairs = r (r<n)

so, the number of ways we can sit n people on r<n chairs is given by

^nC_r=\dfrac{n!}{(n-r)!r!}

c) If there are three awards :

Gold, silver, bronze.

We need to find the number of ways that these medals can be awarded.

Number of ways is given by

^8P_3\\\\=336

d) Number of 5-digit zip codes are possible is given by

^{10}P_5=30240

e) Number of poeple = 10

Number of people required in committee = 3

Number of different 3 person committee that are selected from 10 people is given by

^{10}C_3=120

Hence, a) 720, b) ^nC_r=\dfrac{n!}{(n-r)!r!} c) 336, d) 30240 e) 120.

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H and k are the x and y coordinates of the center of the circle and r is the radius.

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