First term = T(1) is obtained by plugging n = 1 into the formula,
thus First term = 1^2 - 4 = 1 - 4
= 3 (answer)
Out of 8 men, 4 can be selected and lined up in (8 x 7 x 6 x 5) = 1,680 ways.
But within that number, each group of 4 appears in (4 x 3 x 2) = 24 orders.
So there are (1,680 / 24) = 70 different groups of men.
Out of 5 women, 3 can be selected and lined up in (5 x 4 x 3) = 60 ways.
But within that number, each group of 3 appears in (3 x 2) = 6 orders.
So there are (60 / 6) = 10 different groups of women.
Each different group of 70 men can be joined by any of the 10 groups
of women. So the total number of possible subcommittees is (70 x 10) = 700 .
Answer
Good question!
A. false. Even though 5 is usually greater than 2, in this case it is less because it is negative and positives are always greater than negatives.
B. true. Just like the last question, positives are always greater than negatives and even though 8 is usually greater than 3, in this case the 3 is a negative so it is less.
C. true. Think about which number is closer to the number line. When we are talking about negative numbers, the number closer to the number line is greater.
D. false. Same concept as the last question where -12 is closer to the number line than -12.5 so -12 is actually greater.
If you have any additional questions feel free to ask me or your teacher so you can really master what you're learning. :)
