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Total combinations where exactly 7 heads appeared = $\large \frac{10!}{7! \times 3!}$

Total combinations where exactly 8 heads appeared = $\large \frac{10!}{8! \times 2!}$

Total combinations where exactly 9 heads appeared = $\large \frac{10!}{9! \times 1!}$

Total combinations where exactly 10 heads appeared = $\large \frac{10!}{10!}$

Total probability where 1st toss is head = $\bigcup_{i = 7}^{10} \left \{\text{ (Total combinations with exactly i heads * probability of head in 1st toss )/ Total combinations } \right \}$

= $(120 \times \frac{7}{10} + 45 \times \frac{8}{10} + 10 \times \frac{9}{10} + 1) /176 $

= $\large \frac{84 +36 + 9 + 1 } { 176} = $$\large 0.7386$

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