निम्नलिखित का मान ज्ञात कीजिए -
(i) `(16!)/(12!)` , (ii) `(10!)/(4!6!)` , (iii) `(1)/(5!) + 1/(6!) +(1)/(7!)`

Explanation

(i)` (16!)/(12!) = (16.15!)/(12!)` , `[ :. n! = n(n-1)!]`
` = (16 xx 15 xx 14 xx 13 xx 12!)/(12!)`
`= 16 xx 15 xx 14 xx 13= 43680`
(ii)`(10!)/(4!6!) = (0 xx 9 xx 8 xx 7 xx 6!)/(4! xx 6!)`
`= (10 xx 9 xx 8 xx 7)/(4!) = (10 xx 9 xx 8 xx 7)/(4 xx 3 xx 2 xx 1) = 210`
(iii) `(1)/(5!) + 1/(6!) + 1/(7!) = (1)/(5!) + (1)/(6.5!) + 1/(7.6.5!)`
`= 1/(5!) (1+1/6+1/(42))`
`= 1/(120) ((42+ 7 + 1)/(42)) = 1/(120).(50)/(42) = (5)/(504)`