Evaluate \(\frac{n!}{\left(n-r\right)!}\), when
(i) n = 6, r = 2 (ii) n = 9, r = 5
(i) n = 6, r = 2 (ii) n = 9, r = 5
Solution and Explanation
(i) When n = 6, r = 2,
\(\frac{n!}{(n-r)!}=\frac{6!}{(6-2)!}\)
\(=\frac{6!}{4!}=\frac{6\times5\times4!}{4!}\)
\(=30\)
(ii) When n = 9, r = 5,
\(\frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}\)
\(=\frac{9!}{4!}=\frac{9\times8\times7\times6\times5\times4!}{4!}\)
\(=9\times8\times7\times6\times5=15120\)
Top CBSE Class XI Mathematics Questions
- A coin is tossed twice, what is the probability that atleast one tail occurs?
- The relation f is defined by
\(f(x) = \begin{cases} x^2, & \quad 0≤x≤3\\ 3x, & \quad 3≤x≤10 \end{cases}\)
The relation g is defined by
\(g(x) = \begin{cases} x^2, & \quad 0≤x≤2\\ 3x, & \quad 2≤x≤10 \end{cases}\)
Show that f is a function and g is not a function. - Let \(f={(x,\frac {x^2}{1+x^2}):x∈R}\) be a function from R into R. Determine the range of f.
- How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
- In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?
Top CBSE Class XI Questions
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.