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A team of 8 students goes on an excursion, in two cars, of which one

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A team of 8 students goes on an excursion, in two cars, of which one  [#permalink]

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New post 30 Jan 2019, 03:04
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A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A. 120
B. 126
C. 146
D. 156
E. 166

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A team of 8 students goes on an excursion, in two cars, of which one  [#permalink]

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New post 30 Jan 2019, 03:37
1
Bunuel wrote:
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A. 120
B. 126
C. 146
D. 156
E. 166



Hi, Archit3110, the way would be
We have 8 students and the question finally boils down to ways to distribute 8 as 5 and 3 in one grouping and as 4 and 4 in other grouping..
so 8C5 and the remaining three will form a group of 3, and 8C4 and other 4 will automatically make the group of remaing 4..
so 8C5+8C4 = \(\frac{8*7*6}{3*2}+\frac{8*7*6*5}{4*3*2}\)=56+70=126
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A team of 8 students goes on an excursion, in two cars, of which one  [#permalink]

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New post Updated on: 30 Jan 2019, 05:02
Bunuel wrote:
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A. 120
B. 126
C. 146
D. 156
E. 166


total students = 8
total available seats are 9
so
8c5+8c4=56+70=126
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Originally posted by Archit3110 on 30 Jan 2019, 03:25.
Last edited by Archit3110 on 30 Jan 2019, 05:02, edited 1 time in total.
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Re: A team of 8 students goes on an excursion, in two cars, of which one  [#permalink]

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New post 30 Jan 2019, 17:29
Isn't it a permutation problem?
How many ways 8 people can travel in 2 cars- 5 seats in one car and 4 in another.
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Re: A team of 8 students goes on an excursion, in two cars, of which one  [#permalink]

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New post 30 Jan 2019, 18:15
There are 8 students but the available total seats are 9. There will always be one vacant seat in one of the cars. So we're really finding how many ways we can group the 9.

9! / 5! 4! = 126

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Re: A team of 8 students goes on an excursion, in two cars, of which one  [#permalink]

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New post 01 Feb 2019, 17:42
Bunuel wrote:
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A. 120
B. 126
C. 146
D. 156
E. 166


We can call the 5-seat car Car A and the 4-seat car Car B. Therefore, we have two cases to consider:

Case 1: Car A seats 5 and Car B seats 3

Case 2: Car A seats 4 and Car B seats 4

Case 1:

If Car A seats 5 and Car B seats 3, then we have 8C5 x 3C3 = (8 x 7 x 6 x 5 x 4)/(5 x 4 x 3 x 2) x 1 = 8 x 7 = 56 ways for the 8 students to travel in these two cars.

Case 2:

If Car A seats 4 and Car B seats 4, then we have 8C4 x 4C4 = (8 x 7 x 6 x 5)/(4 x 3 x 2) x 1 = 2 x 7 x 5 = 70 ways for the 8 students to travel in these two cars.

So we have a total of 56 + 70 = 126 ways for the 8 students to travel in these two cars.

Answer: B.
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Re: A team of 8 students goes on an excursion, in two cars, of which one   [#permalink] 01 Feb 2019, 17:42
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