Permutations And Combinations

Question
CBSEENMA11014039

How many 5-digit telephone numbers can be constructed, using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ?

Solution

                
 Five of the 10-digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) are to be used.
The number must start with 67.
Number of ways of filling box (v) = 1                                (∵ Only by 6)
rightwards double arrow                       m = 1    
Number of ways of filling box (u) = 1                                (∵ Only by 7)
rightwards double arrow                      n = 1
Number of ways of filling box (z) = 8                        (∵ 6 and 7 are not allowed)
rightwards double arrow                     p = 8     
Number of ways of filling box (y) = 7                      (∵ Repetition is not allowed)
rightwards double arrow                     q = 7
Number of ways of filling box (x) = 6                      (∵ Repetition is not allowed)
rightwards double arrow                     r = 6
∴ Total number of 5-digit telephone numbers formed = m x n x p x q x r = 1 x 1 x 8 x 7 x 6 = 336

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Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.