Three persons A,B,C are to speak at a function along with 7 other persons.If the person speak in random order,the probability that A speaks before B and B speaks before C is

The number of ways in which the following prizes be given to a class of 20 boys, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English is

If a is the number of ways of selecting 3 men from 6 men, b is the number of ways of selecting 2 men, 1 woman from 4 me and 2 women and c is the number of ways of selecting 1 man, 2 women from 3 men and 3 women then the ascending of a,b,c is

A gentleman invites a party of 10 guests to a dinner and places 6 of them at one table and the remaining 4 at another, the tables being around. The number of ways in which he can arrange the guests is

A railway carriage can seat 5 each side.The number of ways a party of 4 girls and 6 boys can seat themselves so that the girls may always have the corner seats is

The number of 4 letters word that can be formed from using the letters of word DELHI which begin and end with an vowel when repetitions are allowed is

If ¹⁵P_r-1 : ¹⁶P_r-2 = 3 : 4 then r =

The number of odd numbers between 1000 and 10000 can be formed with the digits 1,2,3,4,5,6,7,8,9 is

The letters of word VICTORY are permuted in all possible ways and the words thus formed are arranged as in a dictionary.The rank of the word VICTORY is

If ⁽ⁿ⁺¹⁾P₅:ⁿP₆= 2: 7 then n =