Distribution of Identical Objects and Integral Solutions

JEE Main Mathematics · Permutations and Combinations · 13 questions, latest first

• Let A={(a, b, c): a, b, c are non-negative integers and a+b+2 c=22}. Then n( A) is equal to:20264 April, Shift 2 · Q17
• The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is202623 January, Shift 2 · Q7
• 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…202529 January, Shift 1 · Q7
• The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is ____.202528 January, Shift 2 · Q22
• The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is ____.20249 April, Shift 2 · Q23
• The number of ways of getting a sum 16 on throwing a dice four times is ____.20245 April, Shift 1 · Q23
• The number of elements in the set S={(x, y, z): x, y, z ∈ Z, x+2 y+3 z=42, x, y, z ≥ 0} equals ____.20241 February, Shift 1 · Q24
• The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2…202431 January, Shift 2 · Q5
• Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to202429 January, Shift 2 · Q4
• The number of seven digit positive integers formed using the digits 1, 2, 3 and 4 only and sum of the digits equal to 12 is ____.202313 April, Shift 1 · Q22
• The number of triplets (x, y, z), where x, y, z are distinct non negative integers satisfying x+y+z=15, is202311 April, Shift 1 · Q4
• Number of integral solutions to the equation x+y+z=21, where x ≥ 1, y ≥ 3, z ≥ 4, is equal to ____.20231 February, Shift 2 · Q85
• Let A=[a_i j], a_i j ∈ Z ∩[0,4], 1 ≤ i, j ≤ 2. The number of matrices A such that the sum of all entries is a prime number p…202331 January, Shift 2 · Q82