n!Evaluate (n-T. when(i) n - 6, r 2(ii) n 9, r-5.
The expression is given as n ! ( n − r ) ! .
(i)
Substitute 6 for n and 2 for r in the given expression.
n ! ( n − r ) ! = 6 ! ( 6 − 2 ) ! = 6 ! 4 !
To take 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 above term can be written as,
6 × 5 × 4 ! 4 ! = 6 × 5 = 30
Thus, the value of given expression is 30.
(ii)
Substitute 9 for n and 5 for r in the given expression.
n ! ( n − r ) ! = 9 ! ( 9 − 5 ) ! = 9 ! 4 !
To take 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 above term can be written as,
9 × 8 × 7 × 6 × 5 × 4 ! 4 ! = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the value of given expression is 15120.
The expression is given as
(i)
Substitute 6 for n and 2 for r in the given expression.
To take 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 above term can be written as,
Thus, the value of given expression is 30.
(ii)
Substitute 9 for n and 5 for r in the given expression.
To take 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 above term can be written as,
Thus, the value of given expression is 15120.
,
when