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How to Find the Inverse of a Function

13 C 3=…

Question

$^{13} C_{3} =$ ___.

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Solution

$^{n} C_{r} = \frac{n!}{r! (n - r)!} = 286$

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Q. The value of

^{12} C_{2} +^{13} C_{3} +^{14} C_{4} + . . . . . . . . +^{999} C_{989}

Q. Find the product and verify the result for a = 1, b = 2 and c = 3.

(\frac{1}{4} a b c) \times (- 6 b^{2} c) \times (- \frac{1}{3} c^{3})

Q. The value of

100 lim n \to 200 [C_{1} - (1 + \frac{1}{2}) C_{2} + (1 + \frac{1}{2} + \frac{1}{3}) C_{3} - \dots + (- 1)^{n - 1} (1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}) C_{n}]

C_{r} =^{n} C_{r}

)

Q. If the value of

^{12} C_{2} +^{13} C_{3} +^{14} C_{4} + . . . +^{999} C_{989}

^{1000} C_{a} + b

| a + b | =

a + b)

is a single digit integer)

Q. If the value of

^{12} C_{2} +^{13} C_{3} +^{14} C_{4} + . . . +^{999} C_{989}

^{1000} C_{a} + b

| a + b | =

a + b)

is a single digit integer)

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