Answer: a) 720, b)
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](https://tex.z-dn.net/?f=6%21%3D720)
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!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
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](https://tex.z-dn.net/?f=%5E8P_3%5C%5C%5C%5C%3D336)
d) Number of 5-digit zip codes are possible is given by
![^{10}P_5=30240](https://tex.z-dn.net/?f=%5E%7B10%7DP_5%3D30240)
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](https://tex.z-dn.net/?f=%5E%7B10%7DC_3%3D120)
Hence, a) 720, b)
c) 336, d) 30240 e) 120.