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A dinner menu is to be designed out of 5 different starters, 6 identical main courses and 4 distinct desserts. In how many ways menu be designed such that there is atleast one of each of the starters, main courses and desserts?
  • a)
    31 x 6 x 15
  • b)
    32 x 6 x 16
  • c)
    31 x 7 x 15
  • d)
    5 x 6 x 4
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A dinner menu is to be designed out of 5 different starters, 6 identic...
Calculating the number of ways to design the menu


  • Number of ways to choose at least one starter out of 5: 2^5 - 1 = 31 ways

  • Number of ways to choose 6 main courses: 1 way since they are identical

  • Number of ways to choose 4 desserts: 4! = 24 ways


Total number of ways to design the menu


  • Total number of ways = Number of ways to choose starters x Number of ways to choose main courses x Number of ways to choose desserts

  • Total number of ways = 31 x 1 x 24 = 31 x 24 = 744 ways


Final answer


  • Therefore, the correct answer is A: 31 x 6 x 15

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Most Upvoted Answer
A dinner menu is to be designed out of 5 different starters, 6 identic...
This problem can be solved by applying combination(5C1*5C2*5C3*5C4*5C5) *6 *(4C1*4C2*4C3*4C4)after solving this we will get the answer that is 31*6*15
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Community Answer
A dinner menu is to be designed out of 5 different starters, 6 identic...
The problem will be solved using combination
(5C1+5C2+5C3+5C4+5C5)*6*(4C1+4C2+4C3+4C4)
So the combination solved part is
(5+10+10+5+1)*6*(4+6+4+1)
=31*6*15
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A dinner menu is to be designed out of 5 different starters, 6 identical main courses and 4 distinct desserts. In how many ways menu be designed such that there is atleast one of each of the starters, main courses and desserts?a)31 x 6 x 15b)32 x 6 x 16c)31 x 7 x 15d)5 x 6 x 4Correct answer is option 'A'. Can you explain this answer?
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