LRU
asked
in Combinatory
Nov 9, 2021

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1 vote

**There are 4 parts of an encyclopedia which are available in a library which are arranged on the shelf along with other books on a shelf which add up to a total 25 books, if the books are arranged randomly then the number of ways in which the encyclopedia is in the correct order is (the parts need not be beside each other)____**

## 1 Answer

1 vote

Let suppose 4parts of encyclopedia as one . Now, we have 22space to put these 4parts

_1_2_3_4_5.................._21_

We can select like : 22C1 +22C2 +22C3 +22C4

Now to have same order :

Case 1 : one place is chosen to put 4parts, so this can be done only in one way . Say ABCD

Case 2 : Two place is chosen . This can be done in 3ways. i. e, (A )(BCD) or (AB)(CD) or (ABC) (D)

case 3: Three place chosen.

A B CD or AB C D or A BC. D

Case4: 4place is chosen. This can be done in one way.

Therefore, total ways = 22C1×1 +22C2×3 +22C3×3+ 22C4×1

_1_2_3_4_5.................._21_

We can select like : 22C1 +22C2 +22C3 +22C4

Now to have same order :

Case 1 : one place is chosen to put 4parts, so this can be done only in one way . Say ABCD

Case 2 : Two place is chosen . This can be done in 3ways. i. e, (A )(BCD) or (AB)(CD) or (ABC) (D)

case 3: Three place chosen.

A B CD or AB C D or A BC. D

Case4: 4place is chosen. This can be done in one way.

Therefore, total ways = 22C1×1 +22C2×3 +22C3×3+ 22C4×1