Test: Problem Solving- 2 - UPSC MCQ

The number of quadrilaterals that can be formed is ⁶C₄ = (6 x 5 x 4 x 3)/(4 x 3 x 2) = 15.

To find out how many three-digit odd numbers can be formed from the digits 1, 3, 5, 0, and 8, we need to consider the constraints:

1. The number must be three digits long.
2. It must be odd.
3. We can use the digits 1, 3, 5, 0, and 8.

For a number to be odd, its last digit must be odd. Given the digits, we have three choices for the last digit (1, 3, 5) to ensure the number is odd.

For the first digit, we can choose any of the four digits except 0 (because a three-digit number cannot start with 0). This gives us 4 options (1, 3, 5, 8).

For the middle digit, we can choose any of the remaining four digits (after choosing the first and the last, but remembering digits can be reused because it's not specified that digits cannot repeat). This gives us 5 options since all five digits are available for use again.

Therefore, the total number of possible three-digit odd numbers is given by the product of the number of options for each position, which is 4×5×34×5×3.

Let's calculate this:

The total number of three-digit odd numbers that can be formed from the digits 1, 3, 5, 0, and 8 is 60. Therefore, the correct answer is option 2: 60.

When arranging the rings on the fingers, we have three choices for each ring (since each ring can be worn on any of the three fingers). Therefore, the total number of arrangements is 3⁵, which is calculated as follows:

3⁵=3×3×3×3×3=243

So, there are 243 ways to wear five rings on three fingers.

      = 252