Question:
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Updated On: Jan 27, 2026
Hide Solution
Verified By Collegedunia
Solution and Explanation
From a committee of 8 persons, a chairman and a vice chairman are to be chosen in such a way that one person cannot hold more than one position.
Here, the number of ways of choosing a chairman and a vice chairman is the permutation of 8 different objects taken 2 at a time.
Thus, required number of ways =\(^8P_2=\frac{8!}{(8-2)!}=\frac{8!}{6!}\)
\(=\frac{8\times7\times6!}{6!}=8\times7=56\)
Was this answer helpful?
0
0
Top Questions on Permutations
- The number of numbers greater than $5000$, less than $9000$ and divisible by $3$, that can be formed using the digits $0,1,2,5,9$, if repetition of digits is allowed, is
- JEE Main - 2026
- Mathematics
- Permutations
- The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is
- JEE Main - 2026
- Mathematics
- Permutations
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Mathematics
- Permutations
- In how many ways can 5 people be arranged in a row?
- MHT CET - 2025
- Mathematics
- Permutations
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
- BITSAT - 2025
- Mathematics
- Permutations
View More Questions
Questions Asked in CBSE Class XI exam
- Balance the following redox reactions by ion-electron method:
(a)MnO4- (aq) + I - (aq) → MnO2(s) + I2(s) (in basic medium)
(b) MnO4- (aq) + SO2(g) → Mn2+(aq) +HSO4- (aq) (in acidic solution)
(c) H2O2(aq)+Fe2+(aq) → Fe3+ (aq) + H2O (l) (in acidic solution)
(d) Cr2O72-+ SO2(g) → Cr3+ (aq) +SO42- (aq) (in acidic solution)- CBSE Class XI
- Oxidation Number
- Write the resonance structures for SO3 , NO2 and NO3-
- CBSE Class XI
- Kossel-Lewis Approach to Chemical Bonding
- At 700 K, equilibrium constant for the reaction:
\(H_2 (g) + I_2 (g) ⇋ 2HI (g)\)
is 54.8. If 0.5 mol L–1 of HI(g) is present at equilibrium at 700 K, what are the concentration of H2(g) and I2(g) assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700 K?- CBSE Class XI
- Law Of Chemical Equilibrium And Equilibrium Constant
- Find the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17.
- CBSE Class XI
- Statistics
Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
- CBSE Class XI
- Statistics
View More Questions
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.