Question

In how many ways can 4 books be arranged out of 16 books on different subjects?

Answer 1

Given:

• Total number of books = 16
• Number of books used for arrangement = 4

To Find:

• The number of ways 4 books can be arranged out of 16 books on different subjects.

Solution:

We are using the formula of permutation which is given by,

$^np_{r}$ = n!/(n-r)! → {equation 1}

Here n = 16 and r = 4, on substituting the values in equation 1 we get,

⇒ $^{16}c_4$ = 16!/(16-12)! = 16!/12! {subtracting the terms in denominator}

⇒ $^{16}c_4$ = (16×15×14×13×12!)/12! {cancelling 12!}

⇒ $^{16}c_4$ = 16×15×14×13 = 43680 {multiplying the terms}

∴ The number of ways 4 books out 16 books can be arranged = 43680.