Question:
In an examination of $9$ papers a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is
In an examination of $9$ papers a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is
Updated On: Jul 6, 2022
- $255$
- $256$
- $193$
- $319$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The candidate is unsuccessful if he fails in $9$ or $8$ or $7$ or $6$ or $5$ papers.>
$\therefore$ the number of ways to be unsuccessful
$=\,^{9}C_{9}+\,^{9}C_{8}+\,^{9}C_{7}+\,^{9}C_{6}+\,^{9}C_{5}$
$=\,^{9}C_{0}+\,^{9}C_{1}+\,^{9}C_{2}+\,^{9}C_{3}+\,^{9}C_{4}$
$=\frac{1}{2}\left(^{9}C_{0}+\,^{9}C_{1}+\,^{9}C_{2}+\,^{9}C_{3} +......... \,^{9}C_{9}\right)$
$=\frac{1}{2}\left(2^{9}\right)=2^{8}$
$=256$
Was this answer helpful?
0
0
Top Questions on permutations and combinations
If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is $ 4 \_\_\_\_\_$.
- JEE Main - 2025
- Mathematics
- permutations and combinations
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- Mathematics
- permutations and combinations
- The value of the expression \( {}^{47} C_4 + \sum_{j=1}^{5} {}^{52-j} C_3 \) is:
- WBJEE - 2025
- Mathematics
- permutations and combinations
View More Questions
Notes on permutations and combinations
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.