The number of six digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that digits do not repeat and the terminal digits are even, is
A.
144
B.
72
C.
288
D.
720
Answer :
720
Solution :
Terminal digits are the first and last digits.
$$\therefore$$ Terminal digits are even
$$\therefore {1^{st}}$$ place can be filled in 3 ways and last place can be filled in 2 ways and remaining places can be filled in $$^5{P_4} = 120{\text{ ways}}{\text{.}}$$
Hence the number of six digit numbers so that
the terminal digits are even, is $$3 \times 120 \times 2 = 720$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is