Question

let $n$ and $k$ be positive integers such that $n < 10^6$ and \[\binom{13}{13} \binom{14}{13} \binom{15}{13} \dots \binom{52}{13} \binom{53}{13} \binom{54}{13}

Answer 1

The expression for given factorial is attached with the solution as an image.

What is a factorial?

• A whole number's factorial is the result of multiplying the integer by each natural number below it. The sign "!" can be used to indicate a factorial symbolically. Therefore, "n factorial" is denoted by the number n and is the sum of the first n natural integers!
• The product of a whole number n with each subsequent whole number that is less than or equal to n up to 1 is known as its factor. As an illustration, the factorial of 4 is 4 3 2 1, which is 24. It is symbolised by the letter "!" Therefore, the value of 4 is 24.

The required expression is represented in terms of factorial as:

Attached as an image

The expression for given factorial is attached with the solution as an image.

Learn more about factorial here:

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