a. Step 1 No replacements 11 People in Total. Only 5 can be in the Group.

Step 2 5C11

Step 3 11*10*9*8*7*6*5*4*3*2*1/ (11-5) 5*4*3*2*1

Step 4  11*10*9*8*7*6*5*4*3*2*1/ (6*5*4*3*2*1)5*4*3*2*1

Step 5 Divide like terms (6*5*4*3*2*1)

Step 6 11*10*9*8*7/5*4*3*2*1

Step 7 55440/120= 462

Answer 462

b. 11 Students in total 2 Must be Jim And Mary 5 makes a Group

Step 2 Since 2 Must be Jim And Mary we make we take it out of the total number of people and the group 11-2 = 9 and 5-2=3

Step 3 3C9

Step 4 9*8*7*6*5*4*3*2*1/(9-3) 3*2*1

Step 5 9*8*7*6*5*4*3*2*1/6*5*4*3*2*1 *3*2*1

Step 6 Divide like Terms 6*5*4*3*2*1

Step 7 9*8*7/ 3*2*1

Step 8    504/6 =84

Answer 84