Question
The number of ways in which a supervisor can choose four workers out of 10 equally competent workers is ________.
To solve the problem of determining the number of ways to choose four workers out of 10, we employ the concept of combinations where the order of selection does not matter. The formula for combinations is given by:
C(n,r)= n!/r!(n−r)!
Here, n is the total number of items to choose from, and r is the number of items to choose. For this problem, n=10 and r=4. Substituting these values into the formula, we get:
C(10,4)= 10!/4!(10−4)!
= 10×9×8×7/4×3×2×1
= 210
This calculation shows there are 210 different ways to choose four workers from a group of 10. The computed solution falls within the provided range (210, 210), confirming it is both accurate and expected. Therefore, the number of ways to choose the workers is 210.
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Important Questions from Combinations
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books ?
Bob is studying the effect of coral and sponge species on reef ecosystems using experiments in artificial square tanks. In each tank, he places 3 species of corals and 2 species of sponges. If there are 6 species of corals and 5 species of sponges to choose from, the minimum number of tanks required to test all combinations of 3 coral and 2 sponge species is _______
(Answer in integer)
- There are nine species of Impatiens (balsams) found in laterite plateaus of the northern Western Ghats, each with a distinct colour. If a plateau has exactly 6 species, then the number of possible colour combinations in the plateau is __________. (Answer in integer)
- Ten teams participate in a tournament. Every team plays each of the other teams twice. The total number of matches to be played is
- In a box, there are 5 green balls and 10 blue balls. A person picks 6 ballsrandomly. The probability that the person has picked 4 green balls and 2 blueballs is
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