A box contains 4 white balls, 5 black balls and 7 green balls. In how many ways can 4 balls be drawn from the box, if at least one white ball, one black ball and one green ball is to be included in a draw? एक डिब्बे में 4 सफेद गेंदें, 5 काली गेंदें और 7 हरी गेंदें हैं। यदि ड्रॉ में कम से कम एक सफेद गेंद, एक काली गेंद और एक हरी गेंद शामिल की जाती है, तो बॉक्स से 4 गेंदें कितने तरीकों से निकाली जा सकती हैं?

Total ways to draw 4 balls from 16 = 16C4 = 1820. Subtract cases where at least one color is missing. No white: 12C4 = 495. No black: 11C4 = 330. No green: 9C4 = 126. But we subtracted cases where two colors are missing twice, so add back: 8C4 (no white, no black) + 7C4 (no white, no green) + 5C4 (no black, no green) = 70+35+5 = 110. Result = 1820 - (495+330+126) + 110 = 910. Alternatively, count directly: (2,1,1) distributions: 4C2×5C1×7C1 + 4C1×5C2×7C1 + 4C1×5C1×7C2 = 6×5×7 + 4×10×7 + 4×5×21 = 210+280+420 = 910. Option A (900) is close but incorrect.