Find the difference between the number of non-negative integral solutions and positive integral solutions of the equation w + x + y + z = 15a)365b)452c)754d)374e)560Correct answer is option 'B'. Can you explain this answer?

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Find the difference between the number of non-negative integral solutions and positive integral solutions of the equation w + x + y + z = 15

a)
365
b)
452
c)
754
d)
374
e)
560

Correct answer is option 'B'. Can you explain this answer?

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Find the difference between the number of non-negative integral soluti...

Consider w + x + y+ z=15.
This is similar to dividing 15 similar objects between 4 people i.e. n = 15 and r - 4

Non-negative integral solutions imply that each variable can take a value of 0 as well.
Thus, the number of non-negative integral solutions of this equation is equivalent to dividing 15 similar objects among 4

people such that each person can get 0 objects as well.
Number of ways in which this can be done is:

Similarly, positive integral solutions imply that each variable can take a value of at least 1.
Thus, the number of positive integral solutions of this equation is equivalent to dividing 15 similar objects among 4 people such that each person gets at least 1 object.
Number of ways in which this can be done is:

Thus, the difference in the number of solutions = 816 - 364 = 452
Hence, option 2.

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Find the difference between the number of non-negative integral solutions and positive integral solutions of the equation w + x + y + z = 15a)365b)452c)754d)374e)560Correct answer is option 'B'. Can you explain this answer?

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