Question

A shop sells 5 different types of sweets. In how many
different ways a total of 8 sweets can be purchased?
(A) 125
(B) 495
(C) 795
(D) 840
(E) 930

please provide a step wise explanation (if possible without formulas please!)​

Answer 1

Answer:

#love....

Step-by-step explanation:

A simple way would be to check different combinations

1) all of same type - all 5 of any of 8 chocolates, so 5 ways

2) two types-7,1 ; 6,2 ; 5,3 ; so 5*4*3=60 and 4,4 so 5*4/2=10...total 60+10=70

3) three types- 5,2,1 ; 4,3,1, so 5*4*3*2=120 and 6,1,1 ; 4,2,2 ; 3,3,2 so 5*4*3/2*3=90...total 210

4) 4 types - 4,2,1,1 ; 3,2,2,1, so 5*4*3*2/2*2=120, and 3,3,1,1 so 5*4*3*2/(2*2)=30, and 5,1,1,1, so 5*4*3*2/3!=20, and 2,2,2,2, so 5!/4!=5...total 175

5) 5 types - 4,1,1,1,1, so 5*4*3*2/4!=5, and 3,2,1,1,1, so 5*4*3*2/3!=20, and 2,2,2,1,1, so 5!/(3!2!)=10, so 35 ways

Total = 5+70+210+175+35=495

B