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?
A chairman and a vice-chairman are to be chosen from a committee of 8 people in such a way that one person cannot hold more than one position.
The number of ways of choosing a chairman and a vice chairman depends on the number of permutation of 8 different people from which 2 are taken at a time.
The formula to calculate the permutation is,
P n r = n ! ( n − r ) !
Where,n is the number of objects taken r at a time.
Since, there is the permutation of 8 people from which 2 are taken at a time. So,substitute 8 for n and 2 for r in the above formula.
P 8 2 = 8 ! ( 8 − 2 ) ! = 8 ! 6 !
To cancel the common factor from numerator and denominator, factorize the bigger term in factorials.
The formula to calculate the factors of a factorial in terms of factorial itself is,
n ! = n ( n − 1 ) ! n ! = n ( n − 1 ) ( n − 2 ) ! [ n ≥ 2 ] ⋮
The permutation can be written as,
P 8 2 = 8 × 7 × 6 ! 6 ! = 8 × 7 = 56
Thus, the number of ways of choosing a chairman and vice-chairman from the committee of 8 people is 56.
A chairman and a vice-chairman are to be chosen from a committee of 8 people in such a way that one person cannot hold more than one position.
The number of ways of choosing a chairman and a vice chairman depends on the number of permutation of 8 different people from which 2 are taken at a time.
The formula to calculate the permutation is,
Where,n is the number of objects taken r at a time.
Since, there is the permutation of 8 people from which 2 are taken at a time. So,substitute 8 for n and 2 for r in the above formula.
To cancel the common factor from numerator and denominator, factorize the bigger term in factorials.
The formula to calculate the factors of a factorial in terms of factorial itself is,
The permutation can be written as,
Thus, the number of ways of choosing a chairman and vice-chairman from the committee of 8 people is 56.
