Answer:
A. 6 188
B. 749 398
C. 6 188
D. 52 975
E. 20 349
F. 11 316
Explanation:
(a) The shop has 6 types of croissants of which a dozen(12) has to be selected
Therefore n=6, r=12
Repetition of croissants is permitted
And C(n+r-1, r)
C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188
(b) The shop has 6 types of croissants of which three dozen(36) has to be selected
Therefore n=6, r=36
Repetition of croissants is permitted
And C(n+r-1, r)
C(6+36-1, 12) = C(41, 36) = 41!÷ 36!(41-36)! = 41!÷36! 5! = 749 398
(c) The shop has 6 types of croissants of which two dozen(24) has to be selected
Let us first select 2 of each kind which 12 croissants in total. Then we still need to select the remaining 12 croissants
Therefore n=6, r=12
Repetition of croissants is permitted
And C(n+r-1, r)
C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188
(d) The shop has 5 types of croissants of which two dozen(24) has to be selected
Therefore n=5, r=24
Repetition of croissants is permitted
And C(n+r-1, r)
C(5+24-1, 24) = C(28, 24) = 28!÷ 24!(28-24)! = 28!÷24! 4! = 20 475
