Find the number of ways in which 6 objects out of 8 can be arranged so that two particular objects are :

(a) included (b) excluded (Hint : (a) ⁶P₂ x ⁶P₄ (b) ⁶P₆)

122. How many different words can be formed out of letters of words ‘TRIBUNE’ so that:

(i) first letter is a vowel (ii) no two vowels are together

(iii) relative position of vowels and consonants remains unchanged?

 (i) How many different numbers of 6-digits can be formed with the numbers 3, 5, 7, 8, 2, 6?

(ii) How many of them are divisible by 5?

(ii) no two vowels are together ?

(iii) vowels may occupy odd places ?

(i) exactly three flags can be used for a signal?

(ii) at most three flags are to be used for a signal?

(iii) at least three flags are to be used for a signal?