Number of ways of selecting 4 shoes from 10 pairs such that exactly one correct pair is selected is (A) ` .^(10)C_(1) .^(9)C_(2).2^(2)` (B) ` .^(10)C_(1)xx9xx16` (C) . `(( .^(10)C_(1).^(4)P_(2).18xx16)/(4!))` (D) d. `10xx18xx16`

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

The total number of ways of selecting 4 letters from the word NARAYANA is: (A) 10 (B) 9 (C) 12 (D) none of these

(1/4)^(-10)xx(2/5)^(-10)

Evaluate : a. (-1)^(7) b. (-1)^(10) c. (-3)^(3)xx(-2)^(2) d. (-3)^(4)

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2m+1) 2^(n) .

A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to a. ^20 C_(10)xx2^(10) b. ^20 C_(10)xx3^(20) c. ^20 C_(10)xx3^(10) d. ^20 C_(10)xx2^(20)

The value of sum_(r=0)^(10)(r)^(20)C_r is equal to: a. 20(2^(18)+^(19)C_(10)) b. 10(2^(18)+^(19)C_(10)) c. 20(2^(18)+^(19)C_(11)) d. 10(2^(18)+^(19)C_(11))

"^10(C_0)^2 - "^10(C_1)^2 + "^10(C_2)^2 - ...... - ( "^10C_9)^2 + ( "^10C_10)^2=

The number of points of intersection of diagonals which lie within the decagon: ^10 C_2 b. ^10 C_4^ c. ^10 C_6+1 d. 10+^(10)C_2

A bag contains 20 coins. If the probability that the bag contains exactly 4 biased coin is 3/4 and that of exactly 5 biased coin is 2/3, then the probability that all the biased coin are sorted out from bag is exactly 10 draws is 5/(10)(^(16)C_6)/(^(20)C_9)+1/(11)(^(15)C_5)/(^(20)C_9) b. 2/(33)[(^(16)C_6+5^(15)C_5)/(^(20)C_9)] c. 5/(33)(^(16)C_7)/(^(20)C_9)+1/(11)(^(15)C_6)/(^(20)C_9) d. none of these