Find f(t – 3) for f(x) = 4x^2 – 8x + 4.
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The number of combinations of size that you can make with
items is given by the so-called binomial coefficient,
• is the number of ways of permuting
items.
• is the number of ways of permuting all but
of the
items.
Dividing by
then gives the number of ways of permuting only
of the total
items.
• is the number of ways of permuting
items.
Dividing by
then removes all those permutations which contain the same items. We call these combinations.
For this problem we only care about counting combinations.
There are
ways of selecting any 3 girls from the total 6 girls in the entire group of people.
There are
was of selecting any 2 boys from the total 7 boys.
Then there are
ways of choosing a committee of 5 people consisting of 3 girls and 2 boys.
If the next question were, "What is the probability that a committee of 5 randomly selected people consists of 3 girls and 2 boys?", then you would additionally need to compute the number of ways one can make a committee of 5 people from the total 13, which is
Then the probability of selecting such a committee at random is