Q:

A customer ordered fourteen zingers. zingers are placed in packages of​ four, three, or one. in how many different ways can this order be​ filled?

Accepted Solution

A:
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-1If the number of packages of four are: 3Then 4×3=12 zingers.a)So, there will be zero packet of 3.and 2 packs of 1.Since, 12+2×1=14Case-2If the number of packages of four are: 2i.e. 4×2= 8 zingers.a)If number of packages of 3 are: 2i.e. 3×2=6then number of package of 1 have to be 0.b)If number of packages of 3 are: 1i.e. 3×1=3 zingersNumber of packages of 1 zinger will be: 3i.e. 8+3+3=14c)If number of packages of 3 are: 0Then number of packets of 1 will be:  6Case-3If the number of packages of four are: 1a)If number of packages of 3 are: 3i.e. 3×3=9 zingers.Hence, number of packets of 1 have to be: 1b)If number of packages of 3 are: 2i.e. 3×2=6 zingersThen number of packets of 1 have to be: 4c)If number of packages of 3 are: 1i.e. 3×1=3 zingersThen number of packets of 1 have to be: 7d)If number of packages of 3 are: 0i.e. 3×0=0 zingersThen number of packets of 1 have to be: 10Case-4If the number of packages of four are: 0a)If number of packages of 3 are: 4i.e. 3×4=12 zingersThen number of packets of 1 have to be: 2b)If number of packages of 3 are: 3i.e. 3×3=9 zingersThen number of packets of 1 have to be: 5c)If number of packages of 3 are: 2i.e. 3×2=6 zingersThen number of packets of 1 have to be: 8d)If number of packages of 3 are: 1i.e. 3×1=3 zingersThen number of packets of 1 have to be: 11e)If number of packages of 3 are: 0i.e. 3×0=0 zingersThen number of packets of 1 have to be: 14There are total 13 ways of doing so.( 1 from case-13 from case-24 from case-3and 5 from case-4i.e.  1+3+4+5=13 ways )