In How Many Ways Can 7 Books Be Arranged On The Shelf If Three The** correct answer **is (d) 720 ways. the three particular books are considered as one unit. we then arrange the total five units (the one unit of three grouped books and four single books) which gives us 5 factorial ways (120 ways). the 3 books in the one unit can also be arranged in 3 factorial ways (6 ways). The total number of ways to arrange 7 books on a shelf, with the stipulation that 3 specific books must remain together, is 720. this is calculated by treating the 3 books as one block and then arranging that block along with the other books.
In How Many Ways Can 7 Books Be Arranged On The Shelf If Three Answer: explanation: let's solve each part of the problem step by step. ### (i) 3 particular books always stand together 1. **treat the 3 particular books as a single unit or "block."** this reduces the total number of units to arrange from 7 books to: 1 block 4 other books = 5 units. 2. **arrange the 5 units**: \ [ 5! = 120 \text { ways} \] 3. The answer is 7! = 1*2*3*4*5*6*7. the standard solution (=mantra) is this: you can put any of the 7 books in the 1 st position in 7 ways. you can put any of the remaining 6 books in the 2 nd position in 6 ways. you can put any of the remaining 5 books in the 3 rd position in 5 ways. . . . and so on . . .
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