Question

ng bars in Pattern (10). 5. A student distributed 4 toffees to each child. If 'n' is the total number of children, then find out how many toffees, the student would have distributed?​

Answer 1

Answer:

It’s given 10<n<15, which means n=11,12,13,14

When n=11,

r =4(no.of students)

Each student should get at least one toffee, therefore 11-4=7(new value of n)

To find how to distribute those 7 toffees we use the form (n+r-1)C(r-1)

(7+4-1)C(4-1) = 10C3 = (10*9*8)/3*2 = 120

Similarly for n=12,

12-4=8

(8+4-1)C(4-1) = 11C3 = (11*10*9)/(3*2) = 165

For n=13,

13-4=9

(9+4-1)C(4-1)= 12C3 = (12*11*10)/(3*2) = 220

For n=14,

14-4=10

(10+4-1)C(4-1) = 13C3 = (13*12*11)/(3*2)= 286

Therefore,

120+165+220+286=791

Answer 2

Answer:

It’s given 10<n<15, which means n=11,12,13,14

When n=11,

r =4(no.of students)

Each student should get at least one toffee, therefore 11-4=7(new value of n)

To find how to distribute those 7 toffees we use the form (n+r-1)C(r-1)

(7+4-1)C(4-1) = 10C3 = (10*9*8)/3*2 = 120

Similarly for n=12,

12-4=8

(8+4-1)C(4-1) = 11C3 = (11*10*9)/(3*2) = 165

For n=13,

13-4=9

(9+4-1)C(4-1)= 12C3 = (12*11*10)/(3*2) = 220

For n=14,

14-4=10

(10+4-1)C(4-1) = 13C3 = (13*12*11)/(3*2)= 286

Therefore,

120+165+220+286=791

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