A team of 6 people is to be chosen from 8 men and 6 women. Find the number of different teams that may be chosen if (a) there are no restrictions,
(b) there are a husband and wife who must not be seperated,

9514 1404 393

  a) 3003

  b) 1419

Step-by-step explanation:

a) With no restrictions, the problem amounts to counting the number of combinations of 14 people taken 6 at a time. That is ...

  14!/(6!(14-6)!) = 3003 . . . teams with no restrictions

__

b) With the restrictions, there are two cases:

  (i) all 6 people are taken from the 12 that exclude the couple. That number of combinations is ...

  12!/(6!(12-6)!) = 924

  (ii) 4 people are taken from the 12 that exclude the couple, and the couple fills the last two team slots. That number is ...

  12!/(4!(12-4)!) = 495

The sum of the counts of these two cases is ...

  924 +495 = 1419 . . . teams with inseparable couple

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

correct answer:

b.(19,-2)