An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 4 novels, 3 plays, 4 poetry books, and 4 nonfiction books.

Step 1 of 2 : If she wants to include no more than 2 plays, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

Step 2 of 2 : If she wants to include all 4 poetry books, how many different

reading schedules are possible? Express your answer in scientific notation

rounding to the hundredths place.

She wants to pick 10 books. She picks all 4 poetry books and therefore needs

to pick 6 more from the 5+5+7=17 other (non-poetry) books.

So she can pick the remaining 6 (non-poetry) books in (17 CHOOSE 6) = 17C6

= 12376 ways.

For each of the 12376 ways to pick the 10 books to read, she can arrange the

order to read them in -- in (10 POSITION 10)=10P10=10!=3628800 ways.

(17C6)(10!)=12376*3628800 = 4.49×1010

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.