Respuesta :
Answer:
The number of different ways this order can be filled is:
13 ways.
Step-by-step explanation:
A customer ordered fourteen zingers.
zingers are placed in packages of four, three, or one.
Case-1
If the number of packages of four are: 3
Then 4×3=12 zingers.
a)
So, there will be zero packet of 3.
and 2 packs of 1.
Since, 12+2×1=14
Case-2
If the number of packages of four are: 2
i.e. 4×2= 8 zingers.
a)
If number of packages of 3 are: 2
i.e. 3×2=6
then number of package of 1 have to be 0.
b)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Number of packages of 1 zinger will be: 3
i.e. 8+3+3=14
c)
If number of packages of 3 are: 0
Then number of packets of 1 will be: 6
Case-3
If the number of packages of four are: 1
a)
If number of packages of 3 are: 3
i.e. 3×3=9 zingers.
Hence, number of packets of 1 have to be: 1
b)
If number of packages of 3 are: 2
i.e. 3×2=6 zingers
Then number of packets of 1 have to be: 4
c)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Then number of packets of 1 have to be: 7
d)
If number of packages of 3 are: 0
i.e. 3×0=0 zingers
Then number of packets of 1 have to be: 10
Case-4
If the number of packages of four are: 0
a)
If number of packages of 3 are: 4
i.e. 3×4=12 zingers
Then number of packets of 1 have to be: 2
b)
If number of packages of 3 are: 3
i.e. 3×3=9 zingers
Then number of packets of 1 have to be: 5
c)
If number of packages of 3 are: 2
i.e. 3×2=6 zingers
Then number of packets of 1 have to be: 8
d)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Then number of packets of 1 have to be: 11
e)
If number of packages of 3 are: 0
i.e. 3×0=0 zingers
Then number of packets of 1 have to be: 14
There are total 13 ways of doing so.
( 1 from case-1
3 from case-2
4 from case-3
and 5 from case-4
i.e. 1+3+4+5=13 ways )
