Solve using counting methods and use P or C where requiredSo

Solve using counting methods and use P() or C() where required

note : only one question allowed per question

1,. any candidate may recieve any award

imagine we have four places to fill

now , to fulfil above condition we have 3 option for freshmen(f) , 2 for sophomores(so), 4 for juniors(j), 3 for seniors(se)

total ways hence to fill places = 3*2*4*3 = 72

2. only juniors and seniors recieve award ?

4 * 3 ways for j , 3*2 ways for se

hence to fill four places = 4*3 *3*2 = 72ways

3. one person of each class can recieve award

same question as 1 hence 72 is answer

4.1f , 2so , 1 secan recieve awards

hence 3 ways for f *2*1 ways for so , 3 ways fo se

hence

3*2*1*3

=18 ways