A certain committee consists of 17 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.

Step-by-step explanation:

Here, the total number of candidates present in the committee  = 17

The posts for which people are to be elected are:

President, Vice -President and Treasurer  = 3 posts

Now, selecting a person for the post of president has total 17 ways.

⇒ The number of ways a president can be chosen = 17 ways

As, one person cannot hold 2 positions.

So, now the total candidates  = 17 - 1  = 16 people

⇒Selecting a person for the post of Vice -President has total 16 ways.

⇒ The number of ways a vice president can be chosen = 16 ways

Similarly, the number of ways a  Treasurer can be chosen = 15 ways

Combining the three ways, we get:

the number of ways President, Vice -President and Treasurer can be chosen   = 17 x 16 x 15  =  4080 ways

Hence, there are 4080 ways in which these 3 offices be filled.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

step-by-step explanation: