How many ways can you choose 2 books from a shelf of 40 books

Accepted Solution

Answer:Hence, the number of ways of doing so is:                                 780 ways.Step-by-step explanation:We know that if we have to choose r items out of a total of 'n' items then the number of ways of doing so is calculated by the formula of combination as:                              [tex]n_C_r[/tex]which is given by:[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]Here we have to chose 2 books out of a shelf of 40 books.i.e. we have: n=40 and r=2Hence, the number of ways of doing so is:[tex]{40}_C_{2}=\dfrac{40!}{2!\times (40-2)!}\\\\\\{40}_C_2=\dfrac{40!}{2!\times 38!}\\\\\\{40}_C_2=\dfrac{40\times 39\times 38!}{2!\times 38!}\\\\\\{40}_C_2=\dfrac{40\times 39}{2}\\\\\\{40}_C_2=780[/tex]             Hence, the answer is:                    780