If a man and his wife enter a bus in which five seats are vacant,then the number of different ways in which they can be seated is

If $\sum_{i=0}^4 {^{4+i}}C_i + \sum_{j=6}^9 {^{3+j}}C_j = {^x}C_y$ ($x$ is a prime number),then which one of the following is incorrect?

The number of words,with or without meaning,that can be formed by taking $4$ letters at a time from the letters of the word $'SYLLABUS'$ such that two letters are distinct and two letters are alike,is

There are $3$ girls in a class of $10$ students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball,is

How many words can be formed out of the letters of the word '$EDUCATION$' such that vowels occupy the odd positions?