Combination Qs Help:) (1 Viewer)

csi

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Hi guys,

I have the answers to the questions below, but I’m not sure on how to work them out...if anyone could help that would be great:)

1. Find the value of n for which nC7+nC8=21C8 (ANSWER: n=20)

2. If 4 maths books are to be selected from 6 different maths books and 3 English books are to be selected from 5 different English books, how many ways can these books be arranged on a shelf if there are no restrictions? (ANSWER: 756000)

3. 30 girls, including Miss Australia, enter a Miss World Competition. The first six places are announced. How many different announcements are possible if Miss Australia is assured a place in the first six? (ANSWER: 85503600)

Thanks guys!!!
 

B1andB2

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Hi guys,

I have the answers to the questions below, but I’m not sure on how to work them out...if anyone could help that would be great:)

1. Find the value of n for which nC7+nC8=21C8 (ANSWER: n=20)

2. If 4 maths books are to be selected from 6 different maths books and 3 English books are to be selected from 5 different English books, how many ways can these books be arranged on a shelf if there are no restrictions? (ANSWER: 756000)

3. 30 girls, including Miss Australia, enter a Miss World Competition. The first six places are announced. How many different announcements are possible if Miss Australia is assured a place in the first six? (ANSWER: 85503600)

Thanks guys!!!
2. 6C4 x 5C3 x7!
3. 29C5 (since miss australia is already guaranteed a place, you now have 5 to choose from 29 remaining contestants) X 6! (to rearrange)
 
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csi

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2. 6C4 x 5C3 x7!
3. 29C5 (since miss australia is already guaranteed a place, you now have 5 to choose from 29 remaining contestants) X 6! (to rearrange)
thanks for the help, much appreciated:)
 

csi

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1. Expanding the combination you get : You can expand the denominator of the second fraction so you get 7!(n-7)! and then just do basic arithmetic and solve for n
thanks:)
 

CM_Tutor

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Question 1, the easy way...

Recall the addition property:

Taking gives

which we recognise as the LHS of our equation, and so our solution is

 

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