There are 5 seats in a car including the driver’s seat. If 3 out of

1.	There are 5 seats in a car including the driver’s seat. If 3 out of 10 members in a family know driving then in how many ways, 5 persons out of 10 members can be arranged in the car?
Answer» 3 out of 10 members in a family know driving. ∴ On the driver’s seat a member can be place in ³P₁ ways. Now, there are 5 seats in a car including the driver’s seat. The remaining 4 members out of remaining 9 members of the family can be placed in ⁹P₄ ways. ∴ Total permutations of such arrangement = ³P₁ × ⁹P₄ = 3 × (9 × 8 × 7 × 6) = 3 × 3024 = 9072

There are 5 seats in a car including the driver’s seat. If 3 out of 10 members in a family know driving then in how many ways, 5 persons out of 10 members can be arranged in the car?

Answer»

3 out of 10 members in a family know driving.

∴ On the driver’s seat a member can be place in ³P₁ ways.

Now, there are 5 seats in a car including the driver’s seat.
The remaining 4 members out of remaining 9 members of the family can be placed in ⁹P₄ ways.

∴ Total permutations of such arrangement

= ³P₁ × ⁹P₄

= 3 × (9 × 8 × 7 × 6)

= 3 × 3024

= 9072

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There are 5 seats in a car including the driver’s seat. If 3 out of 10 members in a family know driving then in how many ways, 5 persons out of 10 members can be arranged in the car?

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