Pls solve this Illustration 6 86 Find the number of ways in which A A A B B B - Maths - Permutations and Combinations

Question

Pls solve this

Illustration 6 86 Find the number of ways in which A A A B B B can
be placed in the squares of Fig 6 14 as shown, so that no row
remains empty Fig 6 14

Neha Sethi · Accepted Answer

Dear student
If we want to fill AAABBB so that none of R1,R2,R3,R4,R5 remains empty,then we  are to use R2 and  R4 and from R1,R3 and R5 use any boxes of onethe three rows and one box of remaining two rows
Number of ways of selection=
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5ab3e6cfb6307%20png"
style="width: 372px; height: 121px;">
So, required ways of permutations of AAABBB in these 81 ways ofselection=81×6!3!×3!=81×7206×6=1620Note: n!=nn-1n-2
×4×3×2×1nCr=n!r!n-r!
Regards

Pls solve this Illustration 6.86 Find the number of ways in which A A A B B B can be placed in the squares of Fig. 6.14 as shown, so that no row remains empty. Fig. 6.14

Pls solve this

Illustration 6.86 Find the number of ways in which A A A B B B can be placed in the squares of Fig. 6.14 as shown, so that no row remains empty. Fig. 6.14