A Box Contains 2 White Balls, 3 Black Balls And 4 Red Balls. In How M

1.	A Box Contains 2 White Balls, 3 Black Balls And 4 Red Balls. In How Many Ways Can 3 Balls Be Drawn From The Box, If At Least One Black Ball Is To Be Included In The Draw?
Answer» We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black). REQUIRED NUMBER of WAYS=(3C16C2)+(3C26C1)+3C3 = (45 + 18 + 1) =64. We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black). Required number of ways=(3C16C2)+(3C26C1)+3C3 = (45 + 18 + 1) =64.

A Box Contains 2 White Balls, 3 Black Balls And 4 Red Balls. In How Many Ways Can 3 Balls Be Drawn From The Box, If At Least One Black Ball Is To Be Included In The Draw?

Answer»

We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

REQUIRED NUMBER of WAYS=(3C1*6C2)+(3C2*6C1)+3C3 = (45 + 18 + 1) =64.

We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

Required number of ways=(3C1*6C2)+(3C2*6C1)+3C3 = (45 + 18 + 1) =64.