Answer with explanation and formula please a There are 12 pe

Answer with explanation and formula please

a) There are 12 people in the line at the cafeteria. In how many different ways they can stay in the line?
b) Three people from the group of 12 are randomly chosen to be seated first. How many different ways are this group of three selected from the 12? Write the formula and repsone.

Solution

a)
12 people can be formed 12 ! ways, becuase each blank can be filled with start of 12, & next to 11, & next to 10 so on.. Places can be filled in a way 12*11*10*9*8*7*6*5*4*3*2*1 = 479001600 ways

b)

first 3 position are sepearated for 3 people chosen among 12.it can be as 12 C 3. firt 3 positions are seated with 3 positions chosen & the remaining 9 positions are to be arranged with 9 people = 12 C 3 * 9! = 220 * 9! = 79833600 ways