Question

15. An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer. a. How many different choices of ten questions are there? [4 points) b. Suppose the instructions specify that either both questions 1 & 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there? [4 points)

Answer 1

There are fourteen question on Now out of 14 in con choos 1o question 14 weys lie 14! 10! (84-10)! woys 14! 4! X10! way 14 x 13 x 16 x 1 # 24 1,001 way of 1,001 di Herent food choices bo there are question, ten i and 2 are both question question. Now if among ten included to (10-2) = 8 question have Then 12.. out of (14-2) 12 such ore cs Thore choice $) such choires. 495

1 If question ond 2 are both not included. have to Then chose the 10 questions ond we (14-2) 12 questions. of (1260) So, there are such choice 121, 10! (12-10)! = 12! 10! *2! 6 12 711 xlo7 lotte 66. = There one T66 both questions choices هرماسل inclueded. 1 and 2 not are in total there Ote 30, (495+6) = 561 choices for 10 questions where the included either both and 2 no question not included. OR both are of them