The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want attend the party together is a. `2xx\ ^(11)C_7+\ ^(10)C_8` b. `\ ^(10)C_8+\ ^(11)C_7` c. `\ ^(12)C_8-\ ^(10)C_6` d. none of these

A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is 112 b. 140 c. 164 d. none of these

The coefficient of x^8y^(10) in the expansion of (x+y)^(18) is a. \ ^(18)C_8 b. \ ^(18)P_(10) c. 2^(18) d. none of these

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) .

Kanchan has 10 friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in she can invite five friends is a. ^8C_5 b. 2xx^8C_3 c. ^10 C_5-2xx^8C_4 d. none of these

If \ ^n C_(12)=\ \ ^n C_8 then n=

The value of .^(13)C_(7)+.^(13)C_(8)+.^(13)C_(9)+.^(13)C_(10)+.^(13)C_(11)+.^(13)C_(12)+.^(13)C_(13) is equal to

If a cricket team of 11 players is to be selected from 8 batsmen, 6 bowlers, 4 all-rounder and 2 wicket keepers, then Number of selection when 2 particular batsmen dont want to play when a particular bowler will play is (A) .^(17)C_10 + ^(19)C_11 (B) .^(17)C_10 + ^(19)C_11 + ^(17)C_11 (C) . ^(17)C_10 + ^(20)C_11 (D) . ^(19)C_10 + ^(19)C_11

A and B can do a work in 8 days, B and C in 12 days, and A and C in 16 days. In what time can they do it, all working together ?

The number of ways in which the digits of the number 125453752 can be rearranged such that no two 5's come together is (A) (9!)/(3!2!) (B) (7!)/(3!2!) (C) (.^7C_3⋅6!)/(2!) (D) none of these

A fair die is tossed eight times. The probability that a third six is observed in eight throw is (\ ^7C_(10)xx5^7)/(6^7) b. (\ ^7C_2xx5^2)/(6^8) c. (\ ^7C_2xx5^5)/(6^6) d. none of these