Respuesta :
use slot method
2 slots
8 choices for first slot
7 choices for second (since 1 is in 1st slot)
8 times 7=56
56 ways to make 2 person teams
2 slots
8 choices for first slot
7 choices for second (since 1 is in 1st slot)
8 times 7=56
56 ways to make 2 person teams
The first name can be any one of the 8.
For each of those . . .
The second name can be any one of the remaining 7.
Total number of ways that 2 names can be drawn = (8 x 7) = 56 .
But . . .
Each team can be drawn in two different ways . . .
-- Smith first, then Cohen
-- Cohen first, then Smith.
So, among the 56 ways to draw 2 names, you will find
each possible pair of names drawn twice, in the opposite
order.
The number of different 2-member teams is (56 / 2) = 28 .
For each of those . . .
The second name can be any one of the remaining 7.
Total number of ways that 2 names can be drawn = (8 x 7) = 56 .
But . . .
Each team can be drawn in two different ways . . .
-- Smith first, then Cohen
-- Cohen first, then Smith.
So, among the 56 ways to draw 2 names, you will find
each possible pair of names drawn twice, in the opposite
order.
The number of different 2-member teams is (56 / 2) = 28 .