The number of ways in which a committee of 7 members can be formed from 6 teachers, 5 fathers and 4 students in such a way that at least one from each group is included and teachers form the majority among them, is

If $C_0, C_2, \ldots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$, then

$$ \left(C_0+C_1\right)-\left(C_2+C_3\right)+\left(C_4+C_5\right)-\left(C_6+C_7\right)+\ldots= $$

$$ 1+\frac{4}{15}+\frac{4 \cdot 10}{15 \cdot 30}+\frac{4 \cdot 10 \cdot 16}{15 \cdot 30 \cdot 45}+\ldots . .+\infty= $$