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 ?
Let us assume a person climbing the stairs can take one stair or two stairs at a time. How many ways can this person climb a flight of eight stairs?
There are 9 different rock lizard species, each with a unique colour. Lizards of 2 different species sit on a rock at any given time. The number of possible colour combinations of rock lizards seen together on a rock 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)
- The number of different possible ways of forming five intramolecular disulfide bonds with ten cysteine residues of a protein is ________
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