Question

A bag contains $2$ red balls, $3$ white balls and $4$ black balls. In how many ways can $3$ ball be drawn from the bag so that a white ball is always included in it.

• A. $64$
• B. $128$
• C. $32$
• D. None of these

Answer 1

Answer: (A)

$64$

When $1$ white ball is drawn and other $2$ from remaining balls

${=}^3{c}_1{\times }^6{c}_2=45$

When $2$ white ball is drawn and other $1$ from remaining balls

${=}^3{c}_2{\times }^6{c}_1=18$

when all balls are white

${}^3{c}_3=1$

Total $45+18+1=64$