JEE PYQ: Permutation And Combination Question 33
Question 33 - 2019 (08 Apr Shift 2)
The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is:
(1) 288
(2) 360
(3) 306
(4) 310
Show Answer
Answer: (4)
Solution
Starting with 5: $6^3 = 216$. Starting with 44 or 45: $45__: 6 \times 6 = 36$; $44__: 6 \times 6 = 36$. Starting with 43: $432_$ with last digit $> 1$: need $> 4321$. $4322$ to $4325$: digits 2,3,4,5 giving 4. $433_$: $6$ ways. $434_$: $6$. $435_$: $6$. Total starting with 43 after 4321: $4 + 6+6+6 = 22 - $ wait, more carefully: $4321$ excluded, $4322$-$4325$: 4 numbers. $433x$: 6. $434x$: 6. $435x$: 6. Total for $43__$: $4 + 18 = 22$. Grand total $= 216 + 36 + 36 + 22 = 310$.
BETA
