34-38 discrete math

34. A group consists of 10 kids and 2 adults. On a hike, they must form a line with an adult at the front and an adult at the back. How many ways are there to form the line? a. 211! b. 12 ! c. 210! d. 212! 35. How many strings of length 10 over the alphabet {a,b,c,d} have exactly 3 a's? a. (103) b. 47 c. (103)37 d. (103)47 36. Natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that Natasha is one of the leaders? a. (304) b. (294) c. (303) d. (293) 37. How many 14-bit strings are there in which the first bit is 1 and there are exactly five 0 's? a. (135) b. 14(513) c. 21(145) d. (614)(61) 38. Which expression is equal to (127) ? a. P(12,7)/7 ! b. P(12,7)/12 ! c. 7(5)!12! d. 7!12! 34. A group consists of 10 kids and 2 adults. On a hike, they must form a line with an adult at the front and an adult at the back. How many ways are there to form the line? a. 211! b. 12 ! c. 210! d. 212! 35. How many strings of length 10 over the alphabet {a,b,c,d} have exactly 3 a's? a. (103) b. 47 c. (103)37 d. (103)47 36. Natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that Natasha is one of the leaders? a. (304) b. (294) c. (303) d. (293) 37. How many 14-bit strings are there in which the first bit is 1 and there are exactly five 0 's? a. (135) b. 14(513) c. 21(145) d. (614)(61) 38. Which expression is equal to (127) ? a. P(12,7)/7 ! b. P(12,7)/12 ! c. 7(5)!12! d. 7!12!