Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by using the digits 1,2 and 3 only, then the number of elements in the set P is :

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(i) number of numbers created using 1111133 = 5 ! 2 ! 7 ! ​ ⇒ 21 (ii) number of numbers created using 1111223 = 4 ! 2 ! 7 ! ​ ⇒ 105 (iii) number of numbers created using 1112222 = 4 ! 3 ! 7 ! ​ ⇒ 35 Total = 161

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