How many different selections of 4 books can be made from 10 different books, if

(i) there is no restriction

(ii) two particular books are always selected

(iii) two particular books are never selected

Asked by Aaryan | 1 year ago |  35

##### Solution :-

Given:

Total number of books = 10

Total books to be selected = 4

(i) there is no restriction

Number of ways = choosing 4 books out of 10 books

10C4

By using the formula,

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

10C4 = $$\dfrac{10! }{ 4! (10 – 4)!}$$

= 10×3×7

= 210 ways

(ii) two particular books are always selected

Number of ways = select 2 books out of the remaining 8 books as 2 books are already selected.

8C2

By using the formula,

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

8C2 = $$\dfrac{8! }{ 2! (8 – 2)!}$$

= 4×7

= 28 ways

(iii) two particular books are never selected

Number of ways = select 4 books out of remaining 8 books as 2 books are already removed.

8C4

By using the formula,

nCr =$$\dfrac{ n!}{r!(n – r)!}$$

8C4 = $$\dfrac{8! }{ 4! (8 – 4)!}$$

= 7×2×5

= 70 ways

The required no. of ways are 210, 28, 70.

Answered by Sakshi | 1 year ago

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