This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the numbers representing the count of each colour: 5, 4, 3, 2, 1 colours. Step 2: Recognize this as an arithmetic series with first term a=5, common difference d=-1, number of terms n=5. Formula for the sum S_n of the first n terms of an arithmetic series: S_n = (n)/(2) [2a + (n-1)d] Step 3: Substitute the values: S_5 = (5)/(2) [2(5) + (5-1)(-1)] S_5 = (5)/(2) [10 + 4(-1)] S_5 = (5)/(2) [10 - 4] S_5 = (5)/(2) (6) S_5 = 5 × 3 S_5 = 15 Total: 15 colours