$n$ balls each of weight $w$ when weighted in pairs the sum of the weights of all the possible pairs is $120$ when they are weighed in triplets the sum of the weights comes out to be $480$ for all possible triplets, then $n$ is

  • A

    $5$

  • B

    $10$

  • C

    $15$

  • D

    $20$

Similar Questions

A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has no girl? 

How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together

  • [IIT 1977]

The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is

  • [JEE MAIN 2020]

The number of arrangements that can be formed from the letters $a, b, c, d, e,f$ taken $3$ at a time without repetition and each  arrangement containing at least one vowel, is

  • [AIEEE 2012]

In how many ways can one select a cricket team of eleven from $17$ players in which only $5$ players can bowl if each cricket team of $11$ must include exactly $4$ bowlers?