Modern Math

Permutation & Combination

Hard

If all the letters of the word MANAGER are arranged to form 7-letter words (with or without meaning), and all such words are arranged lexicographically (as in a dictionary), how many of these words will precede the word MANAGER?

1518

1514

1512

1516

✅ Correct Option: 2

The letters of MANAGER are A, A, E, G, M, N and R.

Count the arrangements that come before MANAGER:

Case	Count
Starts with A	$6!=720$
Starts with E	$\dfrac{6!}{2!}=360$
Starts with G	$\dfrac{6!}{2!}=360$
Starts with MA and the third letter is A, E or G	$3\times4!=72$
Starts with MANA and the fifth letter is E	$2!=2$

Total $=720+360+360+72+2=1514$ .

2024: Slot 1

Two British and three Indian men and their wives are to be seated around a circular table. If the seating arrangements are defined only by the relative positions of the people, then the total number of ways in which each British man can be seated next to his wife and each Indian man can also be, simultaneously, seated next to his wife is:

2024: Slot 2

Out of 7 different consonants and 4 different vowels, how many words (not necessarily meaningful) of 4 consonants and 2 vowels can be formed?

BBA-DBE Bangalore 2025

A person hosts a party of 13 guests and places 5 of them on one table and the remaining on the other table, the tables being round. In how many ways can he arrange the guests?

If all the letters of the word MANAGER are arranged to form 7-letter words (with or without meaning), and all such words are arranged lexicographically (as in a dictionary), how many of these words will precede the word MANAGER?

Solution

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