Zaheer Khan has taken 4 five-wicket hauls in his last 16 matches. His match records are selected at random, one by one, and analyzed. If none of the match records is analyzed more than once, then what is the probability that the 10th one analyzed is his last five-wicket haul match?⁴𝐶3×12𝐶6¹6𝐶9×17¹ 6 C 9 ⁴C 3 × 12 C 6 × 71 ⁴𝐶3×12𝐶6¹6𝐶9¹ 6 C 9 ⁴C 3 × 12 C 6 ¹2𝐶6¹6𝐶9¹ 6 C 9 ¹ 2 C 6 1771
Question
Zaheer Khan has taken 4 five-wicket hauls in his last 16 matches. His match records are selected at random, one by one, and analyzed. If none of the match records is analyzed more than once, then what is the probability that the 10th one analyzed is his last five-wicket haul match?⁴𝐶3×12𝐶6¹6𝐶9×17¹ 6 C 9 ⁴C 3 × 12 C 6 × 71 ⁴𝐶3×12𝐶6¹6𝐶9¹ 6 C 9 ⁴C 3 × 12 C 6 ¹2𝐶6¹6𝐶9¹ 6 C 9 ¹ 2 C 6 1771
Solution
The problem is asking for the probability that the 10th match analyzed is the last of the four matches in which Zaheer Khan took five wickets.
Here's how to solve it:
Step 1: We first need to select 3 matches out of the 4 five-wicket haul matches. This can be done in 4C3 ways.
Step 2: We also need to select 6 matches out of the remaining 12 matches (16 total matches - 4 five-wicket haul matches = 12 matches). This can be done in 12C6 ways.
Step 3: These 9 matches (3 from step 1 and 6 from step 2) can be arranged in 9! ways. But, the order in which we select the matches doesn't matter, so we divide by 9! to get the number of ways to select and arrange these 9 matches.
Step 4: The 10th match is the last five-wicket haul match, which can be selected in 1 way.
Step 5: The remaining 6 matches can be selected in 6C6 = 1 way.
Step 6: The total number of ways to select and arrange all 16 matches is 16C10.
So, the probability that the 10th match analyzed is the last five-wicket haul match is (4C3 * 12C6 * 1 * 1) / 16C10.
You can calculate the above expression to get the numerical probability.
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