There are 18 chairs in a row (marked 1,2,..., 18) to seat 6 chemistry majors, 5 AMS majors and 7 music majors. (There are no double majors.) Find the number of possible seatings for each of the following:(a). The Chemistry majors must sit in the first 6 seats.(b). The Chemistry majors can not sit in the first 6 seats.(c). The students with the same majors must sit in a "block" (meaning each major sits together).

(a) (b) (c)

Step-by-step explanation:

GIVEN: There are chairs in a row (marked ) to seat chemistry majors, AMS majors and music majors. (There are no double majors).

TO FIND: Find the number of possible seating for each of the following:(a). The Chemistry majors must sit in the first seats.(b). The Chemistry majors can not sit in the first seats.(c). The students with the same majors must sit in a "block" (meaning each major sits together).

SOLUTION:

(a)

as chemistry major first seats, and rest will sit on last seats.

total number of possible seating

(b)

as chemistry major last seats, and rest will sit on first seats.

total number of possible seating

(c)

if the students with the same majors must sit in a block.

then total number of possible seating

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet