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If some three coefficients in the binomial expansion of (x + 1)ⁿ in powers of x are in the ratio 2: 15: 70, then the average of these three coefficients is:

1. 232
2. 964
3. 625
4. 227

Correct answer: 232

Solution

The coefficients in the binomial expansion are given by the binomial formula, and their ratios can be expressed in terms of combinations. By setting up the equations based on the given ratios and solving for the coefficients, we find that their average is 232.

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