In how many ways 4 balls can be picked from 6 black and 4 green colored balls such that at least one black ball is selected?

Question

Aicharya · Accepted Answer

All possible cases if at least one Black ball is selected are,

$1 B 3 G, 2 B 2 G, 3 B 1 G, 4 B 0 G$

Then total number of ways are,

$= {}^{6}{C_{1}} \times {}^{4}{C_{3}} + {}^{6}{C_{2} \times} {}^{4}C_{2} + {}^{6}{C_{3} \times} {}^{4}{C_{1}} + {}^{6}{C_{4}}$

$= 6 \times 4 + 15 \times 6 + 20 \times 4 + 15$

$= 209$

In how many ways 4 balls can be picked from 6 black and 4 green colored balls such that at least one black…