यदि `""^(r+s)P_(2) = 42` तथा `""^(r-s)P_(2) = 20`, तब r व s के मान ज्ञात कीजिए ।

Answer

r = 6, s = 1

Explanation

`""^(r+s)P_(2) = 42 rArr ((r+s)!)/((r+s-2)!) = 42 rArr (r+s)(r+s-1) = 42"………."(i)`
इसी प्रकार `""^(r-s)P_(2) =20 rArr (r-s) (r-s-1) = 20"……."(ii)`
माना `r+s= x`, समीकरण (i) से,
`x(x-1) = 42 = 7xx6rArr x = 7 rArr r+s= 7 "............"(iii)`
माना `r-s = y`,समीकरण (ii) से,
`y(y-1) = 0 rArr y(y-1) = 5 xx 4 rArr y = 5`
`:. r - s = 5"..........."(iv)`
समीकरण (iii) व (iv) से, `r = 6` तथा `s = 1`