Out of 50 basketball players trying to make a team, 5 will be chosen. 36 of the 50 are seniors and the remaining players are juniors. the coach wants 2 seniors and 3 juniors to make the team. in addition, the coach wants a senior who makes the team to be a captain. in how many ways can the coach select such a team from the 50 players who try out?

  5503680

Step-by-step explanation:

The coach wants  2 senior out of 36 so he have

C₃₆,₂   =  36!/( 36 - 2 )!     = 36*35*34!/34!    =  36 * 35   = 1260

possibilities

Now he also wants 3 juniors out of 14

C₁₄,₃  =   14!/ (14- 3)!      =  14*13*12*11!/11!     =  14*13*12  = 2184

Now for each pair of senior (from 1260 outcomes) coach has 2184 possiblities therefore

Coach has

2184 * 1260 = 2751840    possibilities to choose from

Again as there are 2 senior to choose for captain we have to multiply by 2 to get the total  ways the team could be

2751840*2  = 5503680

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47