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Chapter 5: Problem 378

A car will hold 2 in the front seat and 1 in the rear seat. If among 6 persons 2 can drive, than number of ways in which the car can be filled is (a) 10 (b) 20 (c) 30 (d) 40

Short Answer

Expert verified
The total number of ways to fill the car is \[2*5*4=40\] ways. Therefore, the correct answer is (d) 40.

Step by step solution

01

Calculate driver combinations

Since there are 2 drivers among the 6 persons, we can calculate the combinations for placing a driver in the driver's seat. Since we only need 1 driver, there are two (2) ways to choose a driver.
02

Calculate combinations for front passenger seat

Now that we have chosen one driver in step 1, we are left with 5 persons (1 driver and 4 non-drivers) to choose from for the front passenger seat. We have 5 choices for the front passenger seat.
03

Calculate combinations for rear seat

Once the driver and front passenger have been chosen, we are left with 4 persons to choose from for the rear seat (since there are 6 persons in total and 2 are already seated). So we have 4 choices for the rear seat.
04

Calculate the total number of ways to fill the car

Now we need to find the total number of ways to fill the car based on the number of combinations in each step. We multiply the combinations in each step to find the result. Total ways = (Driver combinations) * (Front passenger combinations) * (Rear seat combinations) Total ways = 2 * 5 * 4
05

Find the answer

After performing the calculation, we find that there are \[2*5*4=40\] ways in which the car can be filled. Therefore, the correct answer is (d) 40.

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Most popular questions from this chapter

The number of five digit number that can be formed by using \(1,2,3\) only, such that exactly three digit of the formed numbers are same is (a) 30 (b) 60 (c) 90 (d) 120

How many different words can be formed by the letters of the word MISSISSIPPI in which no two \(S\) are adjacent ? (a) \(8 \times{ }^{6} \mathrm{C}_{4} \times{ }^{7} \mathrm{C}_{4}\) (b) \(2 \times 7 \times{ }^{8} \mathrm{C}_{4}\) (c) \(6 \times 8 \times{ }^{7} \mathrm{C}_{4}\) (d) \(7 \times{ }^{6} \mathrm{C}_{4} \times{ }^{8} \mathrm{C}_{4}\)

if \(a_{n}={ }^{n} \sum_{r=0}\left[1 /\left({ }^{n} C_{r}\right)\right]\) then value of \(^{n} \sum_{r=0}\left[(n-2 r) /\left({ }^{n} C_{r}\right)\right]\) is (a) \((\mathrm{n} / 2) \mathrm{a}_{\mathrm{n}}\) (b) \((1 / 4) \mathrm{a}_{\mathrm{n}}\) (c) \(\mathrm{n} \cdot \mathrm{a}_{\mathrm{n}}\) (d) none of these.

The number of 9 digit numbers formed using the digit 223355888 such that odd digits occupy even places is (a) 16 (b) 36 (c) 60 (d) 80

There are three piles of identical yellow, black, and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls is (a) 6 (b) 7 (c) 8 (d)
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