An urn contains 4 white balls and 7 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 11 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?

(a) 2 white & 1 red ball = 42 ways

(b) All 3 white balls =  4 ways

(c) All 3 red balls = 35 ways

Step-by-step explanation:

An urn contains 4 white balls and 7 red balls. Three balls are selected.

In how many ways can the 3 balls be drawn from a total of 11 balls:

(a) If 2 balls are white and 1 is red?

The 2 white balls can be selected in ⁴C₂ ways

The 1 red ball can be selected in ⁷C₁ ways

2 white & 1 red ball = ⁴C₂ × ⁷C₁

2 white & 1 red ball = 6 × 7

2 white & 1 red ball = 42 ways

(b) If all 3 balls are white?

The 3 white balls can be selected in ⁴C₃ ways

The 0 red ball can be selected in ⁷C₀ ways

All 3 white balls = ⁴C₃ × ⁷C₀

All 3 white balls =  4 × 1

All 3 white balls =  4 ways

(c) If all 3 balls are red?

The 3 red balls can be selected in ⁷C₃ ways

The 0 white ball can be selected in ⁴C₀ ways

All 3 red balls = ⁷C₃ × ⁴C₀

All 3 red balls = 35 × 1

All 3 red balls = 35 ways

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step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

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m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

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