Question

Find r, if 16C4 + 16C5 +17C6 +18C7 = 19Cr​

Answer 1

r = 7

• Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group. It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets.
• The combination is defined as “An arrangement of objects where the order in which the objects The phrase "Selection of things" denotes a situation in which the order in which items are chosen is not significant. Combinations are a subset of permutations in which the order of the choices is ignored. As a result, the number of permutations always exceeds the number of combinations.

Here, according to the given information, we are given that,

$16C_{4} + 16C_{5} + 17C_{6}+18C_{7}= 19C_{r}$

Then, we get,

1820 + 4368 + 12376 + 31824 = 50388 = $19C_{r}$

That is, r = 7.

Hence, r = 7

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