Question 9 of 42beginner🔧 ApplyNumerical2 marks

Compute 8!/(6! × 2!)

Correct Answer

28

Exercise: EXERCISE 6.2 | Q: 3 | (Page 8)
For More Understanding

Explanation

This question follows the same pattern as Example 6(ii) and Example 7 from the textbook. The key technique is to expand the larger factorial in terms of the smaller factorial to enable cancellation. Here, 8! is expanded as 8×78 \times 7 × 6!, which allows the 6! terms to cancel out. The remaining calculation involves dividing by 2! (which equals 2).

Solution Steps

  1. Step 1: Expand 8! in terms of 6! We have 8! = 8×78 \times 7 × 6!

  2. Step 2: Substitute in the given expression 8!/(6! × 2!) = (8×78 \times 7 × 6!)/(6! × 2!)

  3. Step 3: Cancel 6! from numerator and denominator = (8×78 \times 7)/2!

  4. Step 4: Evaluate 2! 2! = 2×12 \times 1 = 2

  5. Step 5: Compute the final value = (8×78 \times 7)/2 = 56/2 = 28

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