To find the number of different committees that the council could choose, we can use combinations (C(n, r)).
We need to choose 3 councillors from a group of 10 councillors, which can be done in C(10, 3) ways. This equals 10! / [(10-3)! * 3!] = 10! / 7! * 3! = (10 * 9 * 8) / (3 * 2 * 1) = 120.
Now, we need to choose either 1 or 2 planning staff to join the committee. This can be done in two ways: (i) selecting only 1 planning staff from a group of 13 or (ii) selecting 2 planning staff from a group of 13.
For Case (i): Choosing 1 planning staff from 13 can be done in C(13, 1) = 13! / [(13 - 1)! * 1!] = 13.
For Case (ii): Choosing 2 planning staff from 13 can be done in C(13, 2) = 13! / [(13 - 2)! * 2!] = (13 * 12) / (2 * 1) = 78.
Now, to find the total number of committees, we sum the numbers of committees in each case:
Total number of committees = Number of committees in Case(i) + Number of committees in Case(ii)
Total number of committees = 13 + 78
Total number of committees = 91
Therefore, the council could choose from 91 different committees.
There are 10 councillors and 13 planning department staff available to serve on a committee to look into re establishing two way traffic on the streets of St. Catharines. If the committee will consist of 3 councillors and either 1 or 2 planning staff, how many different committees could the council choose?
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