JEE Main 2026 · 4 Apr · Shift 1 · Mathematics Q21

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MathematicsInteger+4 / -1Question 21 of 75

A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is $p$ , then $96p$ is equal to ________.

Your answer

Answer and worked solution

Official answer: 9

Split the tosses. Let tosses 1-3 have $a$ heads, 4-6 have $b$ , and 7-8 have $c$ . Then $a+b=4$ and $b+c=3$ .

Count.

$b=1$ : $\binom33\binom31\binom22=3$ .
$b=2$ : $\binom32\binom32\binom21=18$ .
$b=3$ : $\binom31\binom33\binom20=3$ .

Probability. $p=\frac{24}{256}=\frac3{32}$ , so $96p=9$ .

Answer: 9

Topics:Classical probability Combinations

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JEE Main 2026 · 4 Apr · Shift 1, Mathematics question 21