Combination Qs Help:) (1 Viewer)

[csi]

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]

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)

 

[csi]

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

 

[TheShy]

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

 

[csi]

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]

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

 

[csi]

Question 1, the easy way...

Recall the addition property:



Taking gives



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

tysm