{"id":223454,"date":"2025-06-01T17:54:58","date_gmt":"2025-06-01T17:54:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223454"},"modified":"2025-06-01T17:55:00","modified_gmt":"2025-06-01T17:55:00","slug":"find-the-value-of-the-combination-5c2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/find-the-value-of-the-combination-5c2\/","title":{"rendered":"Find the value of the combination. 5C2"},"content":{"rendered":"\n

Find the value of the combination. 5C2<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/mark><\/strong><\/p>\n\n\n\n

The value of the combination 5C2\\mathbf{^5C_2} is: 5C2=5!2!(5\u22122)!=5!2!\u22c53!=1202\u22c56=12012=10^5C_2 = \\frac{5!}{2!(5-2)!} = \\frac{5!}{2! \\cdot 3!} = \\frac{120}{2 \\cdot 6} = \\frac{120}{12} = 10<\/p>\n\n\n\n

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Explanation<\/h3>\n\n\n\n

In mathematics, a combination<\/strong> is a way of selecting items from a larger set where order does not matter<\/strong>. This is different from a permutation, in which the order does<\/strong> matter.<\/p>\n\n\n\n

The notation nCr^nC_r, read as “n choose r”, represents the number of ways to choose r<\/strong> items from a group of n<\/strong> distinct items, without considering the order of selection. The formula for calculating combinations is: nCr=n!r!(n\u2212r)!^nC_r = \\frac{n!}{r!(n – r)!}<\/p>\n\n\n\n

Here, “!”<\/strong> (factorial) denotes the product of all positive integers up to that number. For example, 5!=5\u00d74\u00d73\u00d72\u00d71=1205! = 5 \\times 4 \\times 3 \\times 2 \\times 1 = 120.<\/p>\n\n\n\n

For the problem 5C2^5C_2, we’re choosing 2 items from a set of 5. Applying the formula: 5C2=5!2!(5\u22122)!=1202!\u22c53!=1202\u22c56=12012=10^5C_2 = \\frac{5!}{2!(5-2)!} = \\frac{120}{2! \\cdot 3!} = \\frac{120}{2 \\cdot 6} = \\frac{120}{12} = 10<\/p>\n\n\n\n

So, there are 10 unique ways<\/strong> to choose 2 items from 5 items when the order doesn’t matter.<\/p>\n\n\n\n

To understand this intuitively, suppose we have 5 items labeled A, B, C, D, and E. The possible unique combinations of 2 items are:<\/p>\n\n\n\n