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##### 12. In how many ways can 8 books including 2 on English be arranged on a shelf in such a way that the English books are never together?

Q.48 If { }^{n} C_{3}={ }^{n} C_{12} then the value of n equal to :(a) 4(b) 8(c) 20(d) 12

8. Find the numbers greater than 23000 that can be formed from the digits 12356 without repeating any digit.HINT: The first two digits on L.H.S. will be 23 etc.

2. Write each of the following in the factorial form:iii) 20.19 .18 .17

Q.26 { }^{n} C_{r} is equal to :(a) \frac{n !}{(n-r) ! r !} (b) \frac{n !}{(n-r) !} (c) \frac{n !}{r !} (d) \frac{(n-r) ! r !}{n !}

6. How many words can be formed from the letters of the following words using all letters when no letter is to be repeated:iii) FASTING?

2. Write each of the following in the factorial form: i) 6.5 .4 .