A student is allowed to select at most n books from a collection of (2n + 1) books. If the total number of ways in which he can select at least one book is 63, find the value of n.

A person is permitted to selected at least one and at most n coins from a collection of (2n+1) distinct coins. If the total number of ways in which he can select coins is 255, find the value of ndot

There are p copies each of n different books. Find the number of ways in which a nonempty selection can be made from them.

A team of four students is to be selected from a total of 12 students. The total number of ways in which the team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to a. 220 b. 182 c. 226 d. none of these

The mid value of first (2n + 1 ) consecutive natural number is n + 103/3 Find the value of n.

There are 10 different books in a shelf. The number of ways in which three books can be selected so that exactly two of them are consecutive is

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^2(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !) (c !)^3)

There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is^(2n)C_n-1.

Find the number of ways of selection of at least one vowel and one consonant from the word TRlPLE.

Find the total number of ways of selecting 5 letters from the word INDEPENDENT .

Find the total number of ways of selecting five letters from the word INDEPENDENT.