Suppose the composition of the Senate is 47 Republicans, 52 Democrats, and 1 Independent. A new committee is being formed to study ways to benefit the arts in education. If 3 senators are selected at random to head the committee, find the probability of the following. Enter your answers as fractions or as decimals rounded to 3 decimal places. Part 1 of 3 The group of 3 consists of all Republicans. P (all Republicans) =
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Step 1: Calculate the total number of ways to choose 3 out of 100 people: This can be calculated using the combination formula: ${{100}\choose{3}} = \frac{100!}{3!(100-3)!} = \frac{100*99*98}{3*2*1} = 161700$ Show more…
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