Fill in the chart, find the nth term (algebraic expression) and write the pattern rule
1 answer:
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Answer: The required result is 15.
Step-by-step explanation: We are given to evaluate the following :
"6 choose 4".
Since we are to choose 4 from 6, so we have to use the combination of 6 different things chosen 4 at a time.
We know that
the formula for the combination of n different things chosen r at a time is given by
For the given situation, n = 6 and r = 4.
Therefore, we get
Thus, the required result is 15.
a. The first part asks for how many ways they can be seated together in a row. Therefore we want the permutations of the set of 6 people, or 6 factorial,
6! = 6 5
= 30 4
= 360 2 = 720 possible ways to order 6 people in a row
b. There are two cases to consider here. If the doctor were to sit in the left - most seat, or the right - most seat. In either case there would be 5 people remaining, and hence 5! possible ways to arrange themselves.
5! = 5 4
= 20 3
= 120 1 = 120 possible ways to arrange themselves if the doctor were to sit in either the left - most or right - most seat.
In either case there are 120 ways, so 120 + 120 = Total of 240 arrangements among the 6 people if the doctor sits in the aisle seat ( leftmost or rightmost seat )
c. With each husband on the left, there are 3 people left, all women, that we have to consider here.
3! = 3 2 6 ways to arrange 3 couples in a row, the husband always to the left