counting problem

[skawal]

i am confused about the problem.

[sahilshah1987]

Hi Skawal IS the answer 336?If yes i will try to explain it further.

[skawal]

no boss.actually it was also mine ans too when i make an effort.the Official Answer is 560.Lets try another way.

[sahilshah1987]

Whew! Got it.

3 soups 2 salads 1 coffee 1 tea 8 desserts 7 sandwiches.

From fundamental principle of counting,

total possibilities = (3+2)*(1+1)*8*7=5*2*8*7=560
OR OR
I hadnt considered the tea or coffee thing...

[shahadatme]

Guys I solved it in this way:

Here is four way you can serve the dinner.

Option-1: (Soup, Sandwich, coffee, dessert)
Option-2: (Salad, Sandwich, coffee, dessert)
Option-3: (Soup, Sandwich, Tea, dessert)
Option-4: (Salad, Sandwich, Tea, dessert)

For option-1, we can serve it 3*7*1*8 way
For option-2, we can serve it 2*7*1*8 way
For option-3, we can serve it 3*7*1*8 way
For option-4, we can serve it 2*7*1*8 way

Total number of way to serve the dinner is
=3*7*1*8 + 2*7*1*8 + 3*7*1*8 + 2*7*1*8
=10*56
=560.

[smvo]

# order doesn´t matters
=> Combination problem


2* (3C1*7C1*1C1*8C1)
+
2* (2C1*7C1*1C1*8C1)

[skawal]

i dont understand how you get the 1 tea and 1 coffee.please clear it to me.

[mickgreen58]

@Skawal

The key is the Or in "tea or coffee".

Say you have 7 types of tea and 2 types of coffee.

I told you, for breakfast, you can have either tea or coffee, meaning you can only have one or the other.

I then asked you, how many different drinks can I have for breakfast, you would not say 14 because that would be tea and coffee together and that is not allowed. So it would be 9, you would add because they are literally one group.