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Count the possible combinations of 3 letters chosen from U, V, W, X, Y, Z.The possible combinations of 3 letters are .

Question

Count the possible combinations of 3 letters chosen from U, V, W, X, Y, Z.The possible combinations of 3 letters are .

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Solution

To calculate the number of possible combinations of 3 letters chosen from U, V, W, X, Y, Z, we use the combination formula which is C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose.

Step 1: Identify 'n' and 'r'. Here, n = 6 (U, V, W, X, Y, Z) and r = 3.

Step 2: Substitute n and r in the formula. So, C(6, 3) = 6! / [(6-3)! * 3!].

Step 3: Simplify the factorials. 6! = 654321, (6-3)! = 3! = 321, and 3! = 32*1.

Step 4: Substitute the simplified factorials back into the formula. So, C(6, 3) = (654321) / [(321) * (32*1)].

Step 5: Simplify the equation. The 321 in the numerator and denominator cancel out, leaving us with (654) / (321) = 20.

So, there are 20 possible combinations of 3 letters chosen from U, V, W, X, Y, Z.

This problem has been solved

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