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Permutations Combinations L2-2


11 Find the sum of all the five digit numbers formed by the digits 2, 4, 6, 8, 0 with repetition.
A196110000
B176110000
C156110000
D136110000


12 I forgot my friend’s 7 digit telephone number, but I remembered that the first two digits of the number are either 25 or 53. Also the number is even and the digit 2 appears once. What is the maximum number of trials I have to make before I can contact my friend?
A$56 \times {9^3}$
B$61 \times {9^3}$
C$64 \times {9^3}$
D$96 \times {9^3}$


13How many numbers greater than a billion but less than ${\rm{10}}^{{\rm{10}}} $ can be formed such that the sum of the digits is equal to 3?
A54
B55
C72
D90


14How many six digit numbers are possible by using the digits 1, 2, 3, 4, 5, 6, 7 without repetition such that they are divisible by 12?
A$20 \times 4!$
B$22 \times 4!$
C$24 \times 4!$
D$26 \times 4!$


15 All the possible seven digit numbers are formed by using the digits 1, 2, ........., 7 without repetition. These numbers are then arranged in ascending order. What will be the ${\rm{2884}}^{{\rm{th}}} $ number in the given order?
A5123476
B5123647
C5123674
D5123467


16 In how many ways can a mixed doubles tennis game be arranged from eight married couples, if no husband and wife play in the same game?
A3199960
B4199960
C5199960
D6199960


17 Sixteen persons are to be seated along two sides of a rectangular table with eight chairs on either side. Of these sixteen, Amit, Jaya, Rishi and Neetu with to sit on one side of the table, while Paresh and Sadashiv with to sit on the other, in how many ways can the arrangement be done?
A${}^8{C_4} \times {}^8{C_2} \times 10!$
B${}^8{P_4} \times {}^8{P_2} \times 10! $
C${}^8{C_4} \times {}^8{C_2} \times 10! \times 2$
D${}^8{P_4} \times {}^8{P_2} \times 10! \times 2$


18 Six people A, B, C, D, E and F are to be seated at a circular table. In how many ways can this be done if A must always have either B or C on his immediate left and B must always have either C or D on his immediate left?
A24
B18
C48
D96