Question

3. A 5 grade class composed of 15 girls and 13 boys is trying to wants to play soccer against a different class during their lunch break. They need 11 players to form a team. a) How many ways can they form the team if all students are allowed to be on the team? b) how many ways can they form the team if they need to have 6 girls and 5 boys on the team?

Answer 1

Solution-
15 13 girls Boys total students = 15+13 28. a in first part we have to calculate how many ways so that I1 Pelayers babayers should be choose h=28 r=11 we use this formula no 28CH - T hi 28! 1! (28-11! 9! (h-r)!

28CH 28X27X36X25YQU X337 33 yolo X19X18! "I! XD = 39916800 21, 474, 180 ways hore 111 28 CH

is girls 15C 6 6 girls selected from 15! 6! (15-6)! X ✓ St5x tūX13XJR X11X/XSI. 6XXXXXZXXXIXGP = 5X2X13X13 ISCG 551 soos ways SOOS how S shoa 1305= = selected from 13 boys 13! 5! X (13—5)! X = 13X RX11X1ỐXgX8! 8XXXX XXXX X 8T 13X1LX9 BES = 1287 so total ways ways to selected 6 girls from 15 is- boys boys = 5005X1287 and 5 from 13 total ways 6,441,435 ways
this is the required solution for the given question. We use combination concept in this question.